Partial differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2002
|
| Ausgabe: | [Nachdr.] |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 518 S. graph. Darst. |
| ISBN: | 0521259142 0521277590 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV037237911 | ||
| 003 | DE-604 | ||
| 005 | 20111031 | ||
| 007 | t | ||
| 008 | 110221s2002 d||| |||| 00||| eng d | ||
| 020 | |a 0521259142 |9 0-521-25914-2 | ||
| 020 | |a 0521277590 |9 0-521-27759-0 | ||
| 035 | |a (OCoLC)635874449 | ||
| 035 | |a (DE-599)BVBBV037237911 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-91G | ||
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a MAT 350f |2 stub | ||
| 100 | 1 | |a Wloka, Joseph |d 1929- |e Verfasser |0 (DE-588)136730108 |4 aut | |
| 240 | 1 | 0 | |a Partielle Differentialgleichungen |
| 245 | 1 | 0 | |a Partial differential equations |c J. Wloka |
| 250 | |a [Nachdr.] | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2002 | |
| 300 | |a XI, 518 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021151462&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-021151462 | ||
Datensatz im Suchindex
| _version_ | 1804143846405177344 |
|---|---|
| adam_text | Contents
Preface
ix
I Sobolev spaces
1
§1
Notation, basic properties, distributions
1
/./
Notation
1
1.2
Partition of unity
4
1.3
Régularisation
of functions
8
1.4
Distributions
10
1.5
The support of a distribution
12
1.6
Differentiation and multiplication
14
1.7
Distributions with compact support
18
1.8
Convolution
20
1.9
The Fourier transformation
25
§2
Geometric assumptions for the domain
Ω
35
2.1
Segment and cone properties
36
2.2
The ^- -property of
Ω
38
2.3
(к,
K)-diffeomorphisms and (k, K)-smooth
ßs 47
2.4
Normal transformations
52
2.5
Differentiable manifolds
58
§3
Definitions and density properties for the Sobolev-Slobodeckii spaces W2(Q)
61
3.1
Definition of the Sobolev-Slobodeckii spaces W 2W)
61
3.2
Density properties
64
§4
The transformation theorem and Sobolev spaces on differentiable manifolds
74
4.1
The transformation theorem
75
4.2
Sobolev spaces on differentiable manifolds, and on the frontier
õQofa
(к,
κ)-
smooth region
87
§5
Definition of Sobolev spaces by the Fourier transformation and extension
theorems
90
5.1
Sobolev spaces and the Fourier transformation
91
5.2
Extension theorems
95
{6
Continuous embedding*
aed Sobolev s
lemma
105
Contents
§7
Compact embeddings
112
§8
The trace operator
120
§9
Weak sequential compactness and approximation of derivatives by dif¬
ference quotients
133
II Elliptic differential operators
139
§10
Linear differential operators
139
§11
The
Lopatinskil-Šapiro
condition and examples
148
ƒ/.ƒ
The
Lopatinskii-Šapiro
condition
148
11.2
Examples
157
§12
Fredholm
operators
165
12.1
The Riesz-Schauder spectral theorem (compact operators)
165
12.2
Fredholm
operators
168
12.3
A priori estimates, the Weyl lemma and smoot
hable
operators
180
§13
The main theorem and some theorems on the index of elliptic boundary
value problems
186
13.1
The main theorems for elliptic boundary value problems
186
13.2
The index and spectrum of elliptic boundary value problems
209
§14
Green s formulae
213
14.1
Normal boundary value operators and Dirichelet systems
214
14.2
The first Green formula
219
14.3
Adjoint boundary value operators and boundary value spaces
222
14.4
The second Green formula
231
14.5
The
antidual
operator
Ľ
and the adjoint boundary value problem
235
§15
The adjoint boundary value problem and the connection with the image
space of the original operator
239
§16
Examples
252
III Strongly elliptic differential operators and the method of
variations
261
§17
Gelfand triples, the Lax-Milgram theorem, P-elliptte and F-coercive
operators
261
17.1
Gelfand triples
261
17.2
Representations for functionals on Sobolev spaces
268
/7.3
The Lax-Milgram theorem
271
17.4
V-elliptic and V-coercive forms, solution theorems
273
/7.5
Trie Green operator
275
í
7.6
The concepts V-elliptic and V-coercive for differential operators
279
§18
Agmon s condition
280
§19
Agmon s theorem: conditions for the K-coercion of strongly elliptic
differential operators
290
19.1
The theorems
ofGârding
and Agmon
290
¡9.2
Examples, including the Dirichlet problem for strongly elliptic differential
operators
302
Contents
§20
Regularity of the solutions of strongly elliptic equations
307
§21
The solution theorem for strongly elliptic equations and examples
336
§22
The
Schauder
fixed point theorem and a non-linear problem
361
§23
Elliptic boundary value problems for unbounded regions
370
IV Parabolic differential operators
376
§24
The Bochner integral
376
24.1
Pettis theorem
376
24.2
The Bochner integral
384
§25
Distributions with values in a Hubert space
H
and the space
ЩО,
T)
390
§26
The existence and uniqueness of the solution of a parabolic differential
equation
395
§27
The regularity of solutions of the parabolic differential equation
403
27.1
An abstract regularity theorem
404
27.2
Differentiability with respect to
t
411
27.3
Differentiability with respect to x, respectively
t
414
§28
Examples
423
V Hyperbolic differential operators
434
§29
Existence and uniqueness of the solution
434
§30
Regularity of the solutions of the hyperbolic differential equation
442
30.1
An abstract regularity theorem
442
30.2
Differentiability with respect to
t
445
JOJ
Differentiability with respect to
x
447
§31
Examples
452
VI Difference processes for the calculation of the solution of the
partial differential equation
462
§32
Functional analytic concepts for difference processes
462
§33
Difference processes for elliptic differential equations and for the wave
equation
481
33.1
Some important inequalities
481
33.2
Construction of a difference process for the Dirichlet problem
484
33.3
A difference process for the wave equation in several space variables
488
§34
Evolution equations
4%
34.1
The time-independent case
498
34.2
The time-dependent case
503
34.3
Stability behaviour of the perturbed process
505
34.4
Several step processes
507
References
511
Function and distribution spaces
515
Index
516
|
| any_adam_object | 1 |
| author | Wloka, Joseph 1929- |
| author_GND | (DE-588)136730108 |
| author_facet | Wloka, Joseph 1929- |
| author_role | aut |
| author_sort | Wloka, Joseph 1929- |
| author_variant | j w jw |
| building | Verbundindex |
| bvnumber | BV037237911 |
| classification_rvk | SK 540 |
| classification_tum | MAT 350f |
| ctrlnum | (OCoLC)635874449 (DE-599)BVBBV037237911 |
| discipline | Mathematik |
| edition | [Nachdr.] |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01368nam a2200361 c 4500</leader><controlfield tag="001">BV037237911</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20111031 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110221s2002 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521259142</subfield><subfield code="9">0-521-25914-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521277590</subfield><subfield code="9">0-521-27759-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)635874449</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV037237911</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 350f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Wloka, Joseph</subfield><subfield code="d">1929-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)136730108</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Partielle Differentialgleichungen</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Partial differential equations</subfield><subfield code="c">J. Wloka</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">[Nachdr.]</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 518 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021151462&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-021151462</subfield></datafield></record></collection> |
| id | DE-604.BV037237911 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:54:09Z |
| institution | BVB |
| isbn | 0521259142 0521277590 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021151462 |
| oclc_num | 635874449 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM |
| physical | XI, 518 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Wloka, Joseph 1929- Verfasser (DE-588)136730108 aut Partielle Differentialgleichungen Partial differential equations J. Wloka [Nachdr.] Cambridge [u.a.] Cambridge Univ. Press 2002 XI, 518 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021151462&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wloka, Joseph 1929- Partial differential equations Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 |
| title | Partial differential equations |
| title_alt | Partielle Differentialgleichungen |
| title_auth | Partial differential equations |
| title_exact_search | Partial differential equations |
| title_full | Partial differential equations J. Wloka |
| title_fullStr | Partial differential equations J. Wloka |
| title_full_unstemmed | Partial differential equations J. Wloka |
| title_short | Partial differential equations |
| title_sort | partial differential equations |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021151462&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wlokajoseph partielledifferentialgleichungen AT wlokajoseph partialdifferentialequations |