Boundary value problems for elliptic systems:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Pr.
2005
|
| Edition: | Digital print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 641 S. |
| ISBN: | 9780521430111 0521430119 |
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MARC
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| 245 | 1 | 0 | |a Boundary value problems for elliptic systems |c J. T. Wloka ; B. Rowley ; B. Lawruk |
| 250 | |a Digital print. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Pr. |c 2005 | |
| 300 | |a XIV, 641 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elliptisches System |0 (DE-588)4121184-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elliptisches Randwertproblem |0 (DE-588)4193399-0 |2 gnd |9 rswk-swf |
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| 689 | 1 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 689 | 2 | 0 | |a Elliptisches Randwertproblem |0 (DE-588)4193399-0 |D s |
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| 700 | 1 | |a Rowley, Brian |e Verfasser |4 aut | |
| 700 | 1 | |a Lawruk, Bohan |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804140640597966848 |
|---|---|
| adam_text | Contents
Preface
page
xi
Index of Notation
xiii
PART I: A Spectral Theory of Matrix Polynomials page
1
1
Matrix polynomials
3
1.1
Smith canonical form
4
1.2
Eigenvectors and Jordan chains
8
1.3
Partial spectral pairs
12
1.4
Canonical set of Jordan chains
16
2
Spectral triples for matrix polynomials
23
2.1
Spectral triples
24
2.2
Properties of spectral triples and the
Calderón
projector
28
2.3
Left Jordan chains and a representation for the resolvent
L~ X)
35
2.4
Transformations of matrix polynomials
39
3
Monic matrix polynomials
43
3.1
Standard pairs and triples
43
3.2
Linearization
47
3.3
Representation of a monic matrix polynomial in terms of
a standard pair
51
3.4
Euclidean algorithm in terms of a standard pair
52
3.5
Monic divisors
57
3.6
Monic spectral divisors
58
3.7
Second degree matrix polynomials and examples
61
3.8
Changing from complex to real matrix coefficients
64
4
Further results
72
4.1
The inhomogeneous equation L(d/dt)u
- ƒ 73
4.2
Infinite spectral triples
75
4.3
More on restrictions of spectral pairs
83
4.4
Spectral triples of products
84
4.5
Transformations of products
91
vii
viii Contents
PART II: Manifolds and Vector Bundles
99
5
Manifolds and vector bundles
Ю1
5.1
Background and notation
101
5.2
Manifolds
ИЗ
5.3
The tangent bundle II9
5.4
Submanifolds I24
5.5
Vector fields I30
5.6
Partitions of unity
138
5.7
Vector bundles 142
5.8
Operations on vector bundles
152
5.9
Homotopy property for vector bundles
161
5.10
Riemannian and Hermitian metrics
164
5.11
Manifolds with boundary
168
5.12
Tubular neighbourhoods and collars
172
Differential forms
180
6.1
Differential forms
180
6.2
The exterior derivative
d
182
6.3
The
Poincaré
lemma
189
6.4
Orientation of a vector bundle
192
6.5
Orientation of a manifold
197
6.6
Integration on manifolds
201
6.7
Stokes theorem
206
6.8
Differential operators in vector bundles
209
6.9
The Hodge star operator and the Laplace-de Rham
operator
217
PART III: Pseudo-Differential Operators and Elliptic Boundary
Value Problems
231
7
Pseudo-differential operators on U
233
7.1
Some remarks about generalizing integrals
233
7.2
The classes Sm
236
7.3
Pseudo-differential operator algebra and asymptotics
243
7.4
Transformations of p.d.o. s under a diffeomorphism
252
7.5
Classical symbols
256
7.6
Continuity in Sobolev spaces
260
7.7
Elliptic operators on R
268
7.8
Garding s inequality and some results on the relation
between the operator norm of a p.d.o. and the norm of its
symbol
271
Appendix: summary of definitions and theorems for Sobolev
spaces
278
Contents ix
Pseudo-differential operators on a compact manifold
287
8.1
Background and notation
288
8.2
Pseudo-differential operators on
M
293
8.3
Main symbols and p.d.o. algebra
298
8.4
Classic operators on
M
307
8.5
Definitions for operators in vector bundles
309
8.6
Pseudo-differential operators in vector bundles
313
8.7
Elliptic operators
324
8.8
An illustration: the Hodge decomposition theorem
335
8.9
Limits of pseudo-differential operators
338
8.10
The index of elliptic symbols
344
Elliptic systems on bounded domains in
W
365
9.1
Fredholm
operators and some functional analysis
365
9.2
Elliptic systems of Douglis-Nirenberg type
376
9.3
Boundary operators and the L-condition
387
9.4
The main theorem for elliptic boundary value problems
393
PART IV: Reduction of a Boundary Value Problem to an Elliptic
System on the Boundary
413
10
Understanding the L-condition
415
10.1
Alternative versions of the L-condition
416
10.2
The Dirichlet problem
423
10.3
Matrix polynomials depending on parameters
427
10.4
Homogeneity properties of spectral triples
431
10.5
The classes Ell and BE* ·- : two theorems of
Agranovič
and Dynin
439
10.6
Homotopies of elliptic boundary problems
443
10.7
The classes
Є
and
SS1·-
447
10.8
Comparing the index of two problems having the same
boundary operator
453
10.9
Composition of boundary problems
457
11
Applications to the index
465
11.1
First-order elliptic systems
466
11.2
Higher-order elliptic systems
475
12
BVP s for ordinary differential operators and the connection
with spectral triples
487
12.1
Extension of C°° functions defined on a half-line
488
12.2
Ordinary differential operators on a half-line
491
x
Contents
13
Behaviour of a pseudo-differential operator near a boundary
502
13.1
C00 functions defined on a half-space
502
13.2
The transmission property
510
13.3
Boundary values of a single-layer potential
517
14
The main theorem revisited
525
14.1
Some spaces of distributions on
IR
+ 530
14.2
The spaces
Я5·
539
14.3
The
Calderón
operator for an elliptic operator
544
14.4
Parametrix for an elliptic boundary problem
549
14.5
An application to the index
557
14.6
The main theorem for operators in
З?®1· ,
and the
classes
S1 ·1
562
PART V: An Index Formula for Elliptic Boundary Problems in
the Plane
577
15
Further results on the Lopatinskii condition
579
15.1
Some preliminaries
579
15.2
The degree or winding number on the unit circle
582
15.3
The topological index
585
15.4
Changing from complex to real matrix coefficients
591
16
The index in the plane
595
16.1
A simple form for first-order elliptic systems with real
coefficients
596
16.2
The index formula for first-order elliptic systems with real
coefficients
600
16.3
A fundamental solution for first-order elliptic systems
with constant real coefficients
602
16.4
Index formulas for higher-order systems with real coeffi¬
cients
605
16.5
The index formula for elliptic systems with complex coef¬
ficients and when the boundary operator is pseudo-
differential
615
17
Elliptic systems with
2x2
real coefficients
623
17.1
Homotopy classification
623
17.2
An example: the Neumann BVP for second-order elliptic
operators
627
17.3
An example: the elliptic system for plane elastic defor¬
mations
630
References
635
Index
639
|
| any_adam_object | 1 |
| author | Wloka, Josef Rowley, Brian Lawruk, Bohan |
| author_facet | Wloka, Josef Rowley, Brian Lawruk, Bohan |
| author_role | aut aut aut |
| author_sort | Wloka, Josef |
| author_variant | j w jw b r br b l bl |
| building | Verbundindex |
| bvnumber | BV024620296 |
| classification_rvk | SK 560 |
| ctrlnum | (OCoLC)633200185 (DE-599)BSZ26231469X |
| discipline | Mathematik |
| edition | Digital print. |
| format | Book |
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| id | DE-604.BV024620296 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:03:12Z |
| institution | BVB |
| isbn | 9780521430111 0521430119 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018592327 |
| oclc_num | 633200185 |
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| owner | DE-83 DE-355 DE-BY-UBR |
| owner_facet | DE-83 DE-355 DE-BY-UBR |
| physical | XIV, 641 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| spelling | Wloka, Josef Verfasser aut Boundary value problems for elliptic systems J. T. Wloka ; B. Rowley ; B. Lawruk Digital print. Cambridge Cambridge Univ. Pr. 2005 XIV, 641 S. txt rdacontent n rdamedia nc rdacarrier Randwertproblem (DE-588)4048395-2 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Elliptisches System (DE-588)4121184-4 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Randwertproblem (DE-588)4048395-2 s Elliptische Differentialgleichung (DE-588)4014485-9 s DE-604 Elliptisches System (DE-588)4121184-4 s 1\p DE-604 Elliptisches Randwertproblem (DE-588)4193399-0 s 2\p DE-604 Rowley, Brian Verfasser aut Lawruk, Bohan Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018592327&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wloka, Josef Rowley, Brian Lawruk, Bohan Boundary value problems for elliptic systems Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Elliptisches System (DE-588)4121184-4 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4014485-9 (DE-588)4121184-4 (DE-588)4193399-0 |
| title | Boundary value problems for elliptic systems |
| title_auth | Boundary value problems for elliptic systems |
| title_exact_search | Boundary value problems for elliptic systems |
| title_full | Boundary value problems for elliptic systems J. T. Wloka ; B. Rowley ; B. Lawruk |
| title_fullStr | Boundary value problems for elliptic systems J. T. Wloka ; B. Rowley ; B. Lawruk |
| title_full_unstemmed | Boundary value problems for elliptic systems J. T. Wloka ; B. Rowley ; B. Lawruk |
| title_short | Boundary value problems for elliptic systems |
| title_sort | boundary value problems for elliptic systems |
| topic | Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Elliptisches System (DE-588)4121184-4 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| topic_facet | Randwertproblem Elliptische Differentialgleichung Elliptisches System Elliptisches Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018592327&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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