Lectures on linear partial differential equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2011
|
| Series: | Graduate studies in mathematics
123 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XVII, 410 S. |
| ISBN: | 9780821852842 |
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MARC
| LEADER | 00000nam a2200000 cb4500 | ||
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| 005 | 20211112 | ||
| 007 | t | ||
| 008 | 110713s2011 |||| 00||| eng d | ||
| 020 | |a 9780821852842 |c hbk. |9 978-0-8218-5284-2 | ||
| 035 | |a (OCoLC)753054413 | ||
| 035 | |a (DE-599)BVBBV039136297 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
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| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 100 | 1 | |a Ėskin, Grigorij I. |d 1936- |e Verfasser |0 (DE-588)1015004326 |4 aut | |
| 245 | 1 | 0 | |a Lectures on linear partial differential equations |c Gregory Eskin |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2011 | |
| 300 | |a XVII, 410 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 123 | |
| 650 | 4 | |a Differential equations, Elliptic | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 7 | |a Partial differential equations / Elliptic equations and systems / Boundary value problems for second-order elliptic equations |2 msc | |
| 650 | 7 | |a Partial differential equations / Elliptic equations and systems / Boundary value problems for higher-order elliptic equations |2 msc | |
| 650 | 7 | |a Partial differential equations / Parabolic equations and systems / Initial value problems for higher-order parabolic equations |2 msc | |
| 650 | 7 | |a Partial differential equations / Hyperbolic equations and systems / Wave equation |2 msc | |
| 650 | 7 | |a Partial differential equations / Spectral theory and eigenvalue problems / Scattering theory |2 msc | |
| 650 | 7 | |a Partial differential equations / Hyperbolic equations and systems / Initial value problems for higher-order hyperbolic equations |2 msc | |
| 650 | 7 | |a Partial differential equations / Spectral theory and eigenvalue problems / Asymptotic distribution of eigenvalues and eigenfunctions |2 msc | |
| 650 | 7 | |a Partial differential equations / Pseudodifferential operators and other generalizations of partial differential operators / Pseudodifferential operators |2 msc | |
| 650 | 7 | |a Partial differential equations / Pseudodifferential operators and other generalizations of partial differential operators / Fourier integral operators |2 msc | |
| 650 | 0 | 7 | |a Lineare partielle Differentialgleichung |0 (DE-588)4167708-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Lineare partielle Differentialgleichung |0 (DE-588)4167708-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1184-8 |
| 830 | 0 | |a Graduate studies in mathematics |v 123 |w (DE-604)BV009739289 |9 123 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024154471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024154471&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024154471 | ||
Record in the Search Index
| _version_ | 1804147974130892800 |
|---|---|
| adam_text | Contents
Preface
xv
Acknowledgments
xvi
Chapter I. Theory of Distributions
1
Introduction to Chapters I, II, III
1
§1.
Spaces of infinitely differentiable functions
2
1.1.
Properties of the convolution
2
1.2.
Approximation by C^-functions
3
1.3.
Proof of Proposition
1.1 5
1.4.
Proof of property b) of the convolution
5
§2.
Definition of a distribution
6
2.1.
Examples of distributions
6
2.2.
Regular functionals
7
2.3.
Distributions in a domain
8
§3.
Operations with distributions
9
3.1.
Derivative of a distribution
9
3.2.
Multiplication of a distribution by a C^-function
9
3.3.
Change of variables for distributions
10
§4.
Convergence of distributions
10
4.1.
Delta-like sequences
12
§5.
Regularizations of nonintegrable functions
14
5.1.
Regularization in R1
15
5.2.
Regularization in Rn
17
§6.
Supports of distributions
20
vii
Contents
6.1.
General
form of a distribution with support at
0 20
6.2.
Distributions with compact supports
22
§7.
The convolution of distributions
24
7.1.
Convolution of
ƒ
Є
V and
φ
Є
C^
24
7.2.
Convolution of
ƒ
e
Γ
and
g
Є
£ 26
7.3.
Direct
product of distributions
27
7.4.
Partial hypoellipticity
28
§8.
Problems
30
Chapter II. Fourier Transforms
33
§9.
Tempered distributions
33
9.1.
General form of a tempered distribution
35
§10.
Fourier transforms of tempered distributions
37
10.1.
Fourier transforms of functions in
S
38
10.2.
Fourier transform of tempered distributions
39
10.3.
Generalization of Liouville s theorem
41
§11.
Fourier transforms of distributions with compact supports
42
§12.
Fourier transforms of convolutions
45
§13.
Sobolev
spaces
46
13.1.
Density of
Cg0
(R )
in Ha(Rn)
49
13.2.
Multiplication by a{x)
Є
S
50
13.3.
Sobolev s embedding theorem
51
13.4.
An equivalent norm for
noninteger
52
13.5.
Restrictions to
hyperplanes
(traces)
53
13.6.
Duality of Sobolev spaces
54
13.7.
Invariance
of Hs(Rn) under changes of variables
55
§14.
Singular supports and wave front sets of distributions
57
14.1.
Products of distributions
61
14.2.
Restrictions of distributions to a surface
63
§15.
Problems
65
Chapter III. Applications of Distributions to Partial Differential
Equations
69
§16.
Partial differential equations with constant coefficients
69
16.1.
The heat equation
70
16.2.
The
Schrödinger
equation
72
16.3.
The wave equation
73
16.4.
Fundamental solutions for the wave equations
74
16.5.
The Laplace equation
78
Contents ix
16.6.
The reduced wave equation
81
16.7.
Faddeev s fundamental solutions for
(—
Δ
—
к2)
84
§17.
Existence of a fundamental solution
85
§18.
Hypoelliptic equations
87
18.1.
Characterization of hypoelliptic polynomials
89
18.2.
Examples of hypoelliptic operators
90
§19.
The radiation conditions
91
19.1.
The Helmholtz equation in R3
91
19.2.
Radiation conditions
93
19.3.
The stationary phase lemma
95
19.4.
Radiation conditions for
π
> 2 98
19.5.
The limiting amplitude principle
101
§20.
Single and double layer potentials
102
20.1.
Limiting values of double layers potentials
102
20.2.
Limiting values of normal derivatives of single layer
potentials
106
§21.
Problems
107
Chapter IV. Second Order Elliptic Equations in Bounded Domains 111
Introduction to Chapter IV 111
§22.
Sobolev spaces in domains with smooth boundaries
112
о
22.1.
The spaces
НЅ(П)
and
#β(Ω)
112
22.2.
Equivalent norm in
Hm(Çl)
113
22.3.
The density of C^ in
Нѕ(п)
114
22.4.
Restrictions to
дп
115
22.5.
Duality of Sobolev spaces in
Ω
116
§23.
Dirichlet problem for second order elliptic PDEs
117
23.1.
The main inequality
118
о
23.2.
Uniqueness and existence theorem in H (Q.)
120
23.3.
Nonhomogeneous Dirichlet problem
121
§24.
Regularity of solutions for elliptic equations
122
24.1.
Interior regularity
123
24.2.
Boundary regularity
124
§25.
Variational approach. The Neumann problem
125
25.1.
Weak solution of the Neumann problem
127
25.2.
Regularity of weak solution of the Neumann problem
128
§26.
Boundary value problems with distribution boundary data
129
x
Contents
26.1.
Partial hypoellipticity
property of elliptic equations
129
26.2.
Applications to nonhomogeneous Dirichlet and Neumann
problems
132
§27.
Variational inequalities
134
27.1.
Minimization of a quadratic functional on a convex set.
134
27.2.
Characterization of the minimum point
135
§28.
Problems
137
Chapter V. Scattering Theory
141
Introduction to Chapter V
141
§29.
Agmon s estimates
142
§30.
Nonhomogeneous
Schrödinger
equation
148
30.1.
The case of q{x)
=
O(^^+a+J
148
30.2.
Asymptotic behavior of outgoing solutions (the case of
)4^) a>0) 149
30.3.
The case of q(x)
=
θ((1+|^|)1+£)
149
§31.
The uniqueness of outgoing solutions
151
31.1.
Absence of discrete spectrum for k2
> 0 155
31.2.
Existence of outgoing fundamental solution (the case of
§32.
The limiting absorption principle
157
§33.
The scattering problem
160
33.1.
The scattering problem (the case of q(x)
=
O(,1,, n+a))
160
33.2.
Inverse scattering problem (the case of q(x)
—
Q(
,χ Λη+α))
162
33.3.
The scattering problem (the case of q(x)
=
О((1+|]|)1+г))
163
33.4.
Generalized distorted plane waves
164
33.5.
Generalized scattering amplitude
164
§34.
Inverse boundary value problem
168
34.1.
Electrical impedance tomography
171
§35.
Equivalence of inverse
В
VP
and inverse scattering
172
§36.
Scattering by obstacles
175
36.1.
The case of the Neumann conditions
179
36.2.
Inverse obstacle problem
179
§37.
Inverse scattering at a fixed energy
181
37.1.
Relation between the scattering amplitude and the Faddeev s
scattering amplitudes
181
Contents xi
37.2.
Analytic continuation of Tr
184
37.3.
The limiting values of Tr and Faddeev s scattering amplitude
187
37.4.
Final step: The recovery of q(x)
190
§38.
Inverse backscattering
191
38.1.
The case of real-valued potentials
192
§39.
Problems
193
Chapter VI. Pseudodifferential Operators
197
Introduction to Chapter VI
197
§40.
Boundedness and composition of ^do s
198
40.1.
The boundedness theorem
198
40.2.
Composition of V do s
199
§41.
Elliptic operators and parametrices
204
41.1.
Parametrix for a strongly elliptic operator
204
41.2.
The existence and uniqueness theorem
206
41.3.
Elliptic regularity
206
§42.
Compactness and the
Fredholm
property
207
42.1.
Compact operators
207
42.2.
Fredholm
operators
208
42.3.
Fredholm
elliptic operators in R
211
§43.
The adjoint of a pseudodifferential operator
211
43.1.
A general form of ^do s
211
43.2.
The adjoint operator
214
43.3.
Weyl s Vdo s
215
§44.
Pseudolocal
property and
microlocal
regularity
215
44.1.
The Schwartz kernel
215
44.2.
Pseudolocal
property of ^do s
217
44.3.
Microlocal
regularity
218
§45.
Change-of-variables formula for ^do s
221
§46.
The Cauchy problem for parabolic equations
223
46.1.
Parabolic
^do s
223
46.2.
The Cauchy problem with zero initial conditions
225
46.3.
The Cauchy problem with nonzero initial conditions
226
§47.
The heat kernel
228
47.1.
Solving the Cauchy problem by Fourier-Laplace transform
228
47.2.
Asymptotics of the heat kernel as
t
-> +0. 230
§48.
The Cauchy problem for strictly hyperbolic equations
231
48.1.
The main estimate
233
xii
Contents
48.2.
Uniqueness and parabolic regularization
235
48.3.
The Cauchy problem on a finite time interval
237
48.4.
Strictly hyperbolic equations of second order
240
§49.
Domain of dependence
243
§50.
Propagation of singularities
247
50.1.
The null-bicharacteristics
247
50.2.
Operators of real principal type
247
50.3.
Propagation of singularities for operators of real principal
type
249
50.4.
Propagation of singularities in the case of a hyperbolic
Cauchy problem
255
§51.
Problems
258
Chapter
VII.
Elliptic Boundary Value Problems and Parametrices
263
Introduction to Chapter
VII
263
§52.
Pseudodifferential operators on a manifold
264
52.1.
Manifolds and vector bundles
264
52.2.
Definition of a pseudodifferential operator on a manifold
265
52.3.
Elliptic i/^do s on a manifold
266
§53.
Boundary value problems in the half-space
266
53.1.
Factorization of an elliptic symbol
266
53.2.
Explicit solution of the boundary value problem
268
§54.
Elliptic boundary value problems in a bounded domain
270
54.1.
The method of freezing coefficients
270
54.2.
The
Fredholm
property
273
54.3.
Invariant form of the ellipticity of boundary conditions
276
54.4.
Boundary value problems for elliptic systems of differential
equations
276
§55.
Parametrices for elliptic boundary value problems
278
55.1.
Plus-operators and minus-operators
278
55.2.
Construction of the parametrix in the half-space
281
55.3.
Parametrix in a bounded domain
284
§56.
The heat trace asymptotics
285
56.1.
The existence and the estimates of the resolvent
285
56.2.
The parametrix construction
286
56.3.
The heat trace for the Dirichlet Laplacian
288
56.4.
The heat trace for the Neumann Laplacian
293
56.5.
The heat trace for the elliptic operator of an arbitrary order
294
§57.
Parametrix for the Dirichlet-to-Neumann operator
296
Contents xiii
57.1.
Construction
of the parametrix
296
57.2.
Determination of the metric on the boundary
300
§58.
Spectral theory of elliptic operators
301
58.1.
The nonselfadjoint case
301
58.2.
Trace class operators
302
58.3.
The selfadjoint case
305
58.4.
The case of a compact manifold
309
§59.
The index of elliptic operators in W1
311
59.1.
Properties of
Fredholm
operators
311
59.2.
Index of an elliptic
ψάο
313
59.3.
Fredholm
elliptic
^do s
in
R
316
59.4.
Elements of If-theory
317
59.5.
Proof of the index theorem
321
§60.
Problems
324
Chapter
VIII.
Fourier Integral Operators
329
Introduction to Chapter
VIII 329
§61.
Boundedness of Fourier integral operators
(FIO
s)
330
61.1.
The definition of
a FIO
330
61.2.
The boundedness of FIO s
331
61.3.
Canonical transformations
333
§62.
Operations with Fourier integral operators
334
62.1.
The stationary phase lemma
334
62.2.
Composition of a ^do and
a FIO
335
62.3.
Elliptic FIO s
337
62.4.
Egorov s theorem
338
§63.
The wave front set of Fourier integral operators
340
§64.
Parametrix for the hyperbolic Cauchy problem
342
64.1.
Asymptotic expansion
342
64.2.
Solution of the eikonal equation
344
64.3.
Solution of the transport equation
346
64.4.
Propagation of singularities
348
§65.
Global Fourier integral operators
349
65.1.
Lagrangian manifolds
349
65.2.
FIO s with
nondegenerate
phase functions
350
65.3.
Local coordinates for a graph of a canonical transformation
353
65.4.
Definition of a global
FIO
358
65.5.
Construction of a global
FIO
given a global canonical
transformation
360
xiv Contents
65.6.
Composition
of global
FIO
s
365
65.7.
Conjugation by a global
FIO
and the boundedness theorem
369
§66.
Geometric optics at large
370
66.1.
Generating functions and the Legendre transforms
370
66.2.
Asymptotic solutions
374
66.3.
The Maslov index
377
§67.
Oblique derivative problem
381
67.1.
Reduction to the boundary
381
67.2.
Formulation of the oblique derivative problem
382
67.3.
Model problem
384
67.4.
First order differential equations with symbols depending
on x
387
67.5.
The boundary value problem on
ΟΩ
394
§68.
Problems
399
Bibliography
403
Index
407
This book is a reader-friendly, relatively short introduction to the modern theory
of linear partial differential equations. An effort has been made to present complete
proofs in an accessible and self-contained form.
The first three chapters are on elementary distribution theory and Sobolev spaces
with many examples and applications to equations with constant coefficients.The
following chapters study the Cauchy problem for parabolic and hyperbolic equa¬
tions, boundary value problems for elliptic equations, heat trace asymptotics, and
scattering theory. The book also covers
microlocal
analysis, including the theory of
pseudodifferential and Fourier integral operators, and the propagation of singulari¬
ties for operators of real principal type. Among the more advanced topics are the
global theory of Fourier integral operators and the geometric optics construction
in the large, the Atiyah-Singer index theorem in W and the oblique derivative
problem.
|
| any_adam_object | 1 |
| author | Ėskin, Grigorij I. 1936- |
| author_GND | (DE-588)1015004326 |
| author_facet | Ėskin, Grigorij I. 1936- |
| author_role | aut |
| author_sort | Ėskin, Grigorij I. 1936- |
| author_variant | g i ė gi giė |
| building | Verbundindex |
| bvnumber | BV039136297 |
| classification_rvk | SK 560 SK 540 |
| ctrlnum | (OCoLC)753054413 (DE-599)BVBBV039136297 |
| dewey-full | 515.3533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3533 |
| dewey-search | 515.3533 |
| dewey-sort | 3515.3533 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV039136297 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T23:59:45Z |
| institution | BVB |
| isbn | 9780821852842 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024154471 |
| oclc_num | 753054413 |
| open_access_boolean | |
| owner | DE-634 DE-824 DE-188 DE-703 DE-19 DE-BY-UBM DE-20 DE-355 DE-BY-UBR DE-11 DE-739 |
| owner_facet | DE-634 DE-824 DE-188 DE-703 DE-19 DE-BY-UBM DE-20 DE-355 DE-BY-UBR DE-11 DE-739 |
| physical | XVII, 410 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Ėskin, Grigorij I. 1936- Verfasser (DE-588)1015004326 aut Lectures on linear partial differential equations Gregory Eskin Providence, RI American Math. Soc. 2011 XVII, 410 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 123 Differential equations, Elliptic Differential equations, Partial Partial differential equations / Elliptic equations and systems / Boundary value problems for second-order elliptic equations msc Partial differential equations / Elliptic equations and systems / Boundary value problems for higher-order elliptic equations msc Partial differential equations / Parabolic equations and systems / Initial value problems for higher-order parabolic equations msc Partial differential equations / Hyperbolic equations and systems / Wave equation msc Partial differential equations / Spectral theory and eigenvalue problems / Scattering theory msc Partial differential equations / Hyperbolic equations and systems / Initial value problems for higher-order hyperbolic equations msc Partial differential equations / Spectral theory and eigenvalue problems / Asymptotic distribution of eigenvalues and eigenfunctions msc Partial differential equations / Pseudodifferential operators and other generalizations of partial differential operators / Pseudodifferential operators msc Partial differential equations / Pseudodifferential operators and other generalizations of partial differential operators / Fourier integral operators msc Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Lineare partielle Differentialgleichung (DE-588)4167708-0 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1184-8 Graduate studies in mathematics 123 (DE-604)BV009739289 123 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024154471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024154471&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Ėskin, Grigorij I. 1936- Lectures on linear partial differential equations Graduate studies in mathematics Differential equations, Elliptic Differential equations, Partial Partial differential equations / Elliptic equations and systems / Boundary value problems for second-order elliptic equations msc Partial differential equations / Elliptic equations and systems / Boundary value problems for higher-order elliptic equations msc Partial differential equations / Parabolic equations and systems / Initial value problems for higher-order parabolic equations msc Partial differential equations / Hyperbolic equations and systems / Wave equation msc Partial differential equations / Spectral theory and eigenvalue problems / Scattering theory msc Partial differential equations / Hyperbolic equations and systems / Initial value problems for higher-order hyperbolic equations msc Partial differential equations / Spectral theory and eigenvalue problems / Asymptotic distribution of eigenvalues and eigenfunctions msc Partial differential equations / Pseudodifferential operators and other generalizations of partial differential operators / Pseudodifferential operators msc Partial differential equations / Pseudodifferential operators and other generalizations of partial differential operators / Fourier integral operators msc Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd |
| subject_GND | (DE-588)4167708-0 (DE-588)4123623-3 |
| title | Lectures on linear partial differential equations |
| title_auth | Lectures on linear partial differential equations |
| title_exact_search | Lectures on linear partial differential equations |
| title_full | Lectures on linear partial differential equations Gregory Eskin |
| title_fullStr | Lectures on linear partial differential equations Gregory Eskin |
| title_full_unstemmed | Lectures on linear partial differential equations Gregory Eskin |
| title_short | Lectures on linear partial differential equations |
| title_sort | lectures on linear partial differential equations |
| topic | Differential equations, Elliptic Differential equations, Partial Partial differential equations / Elliptic equations and systems / Boundary value problems for second-order elliptic equations msc Partial differential equations / Elliptic equations and systems / Boundary value problems for higher-order elliptic equations msc Partial differential equations / Parabolic equations and systems / Initial value problems for higher-order parabolic equations msc Partial differential equations / Hyperbolic equations and systems / Wave equation msc Partial differential equations / Spectral theory and eigenvalue problems / Scattering theory msc Partial differential equations / Hyperbolic equations and systems / Initial value problems for higher-order hyperbolic equations msc Partial differential equations / Spectral theory and eigenvalue problems / Asymptotic distribution of eigenvalues and eigenfunctions msc Partial differential equations / Pseudodifferential operators and other generalizations of partial differential operators / Pseudodifferential operators msc Partial differential equations / Pseudodifferential operators and other generalizations of partial differential operators / Fourier integral operators msc Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd |
| topic_facet | Differential equations, Elliptic Differential equations, Partial Partial differential equations / Elliptic equations and systems / Boundary value problems for second-order elliptic equations Partial differential equations / Elliptic equations and systems / Boundary value problems for higher-order elliptic equations Partial differential equations / Parabolic equations and systems / Initial value problems for higher-order parabolic equations Partial differential equations / Hyperbolic equations and systems / Wave equation Partial differential equations / Spectral theory and eigenvalue problems / Scattering theory Partial differential equations / Hyperbolic equations and systems / Initial value problems for higher-order hyperbolic equations Partial differential equations / Spectral theory and eigenvalue problems / Asymptotic distribution of eigenvalues and eigenfunctions Partial differential equations / Pseudodifferential operators and other generalizations of partial differential operators / Pseudodifferential operators Partial differential equations / Pseudodifferential operators and other generalizations of partial differential operators / Fourier integral operators Lineare partielle Differentialgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024154471&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024154471&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT eskingrigoriji lecturesonlinearpartialdifferentialequations |