Distributions, Sobolev spaces, elliptic equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Zürich
European Math. Soc.
2008
|
| Schriftenreihe: | EMS textbooks in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 294 S. graph. Darst. |
| ISBN: | 9783037190425 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
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| 008 | 080611s2008 d||| |||| 00||| eng d | ||
| 020 | |a 9783037190425 |9 978-3-03719-042-5 | ||
| 035 | |a (OCoLC)254092397 | ||
| 035 | |a (DE-599)HEB194266001 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-824 |a DE-355 |a DE-91G |a DE-384 |a DE-11 |a DE-83 |a DE-188 |a DE-19 |a DE-20 |a DE-739 |a DE-29T | ||
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| 100 | 1 | |a Haroske, Dorothee |d 1968- |e Verfasser |0 (DE-588)118052489 |4 aut | |
| 245 | 1 | 0 | |a Distributions, Sobolev spaces, elliptic equations |c Dorothee D. Haroske ; Hans Triebel |
| 264 | 1 | |a Zürich |b European Math. Soc. |c 2008 | |
| 300 | |a IX, 294 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS textbooks in mathematics | |
| 650 | 0 | 7 | |a Sobolev-Raum |0 (DE-588)4055345-0 |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 Distribution |g Funktionalanalysis |0 (DE-588)4070505-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Distribution |g Funktionalanalysis |0 (DE-588)4070505-5 |D s |
| 689 | 0 | 1 | |a Sobolev-Raum |0 (DE-588)4055345-0 |D s |
| 689 | 0 | 2 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Triebel, Hans |d 1936- |e Verfasser |0 (DE-588)133515923 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |a Haroske, Dorothee, 1968- |t Distributions, Sobolev spaces, elliptic equations |n Online-Ausgabe |z 978-3-03719-542-0 |w (DE-604)BV036713224 |
| 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=016522606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016522606 | ||
Datensatz im Suchindex
| _version_ | 1804137690719846400 |
|---|---|
| adam_text | Contents
Preface
v
1
The Laplace-Poisson equation
1
1.1
Introduction, basic definitions, and plan of the book
........ 1
1.2
Fundamental solutions and integral representations
........ 3
1.3
Green s functions
.......................... 6
1.4
Harmonic functions
......................... 10
1.5
The Dirichlet problem
........................ 17
1.6
The
Poisson
equation
........................ 20
1.7
Notes
................................ 23
2
Distributions
25
2.1
The spaces
£>(Ω)
and
£> (Ώ)
.................... 25
2.2
Regular distributions, further examples
............... 27
2.3
Derivatives and multiplications with smooth functions
....... 31
2.4
Localisations, the spaces
6 (Ω)
................... 33
2.5
The space
-8(Џ ),
the Fourier transform
.............. 38
2.6
The space
Ѕ (Џп)
.......................... 43
2.7
The Fourier transform in
£ (№. ).................. 47
2.8
The Fourier transform in LpflR )
.................. 49
2.9
Notes
................................ 53
3
Sobolev spaces on R and R^.
56
3.1
The spaces w£(Rn)
......................... 56
3.2
The spaces Hs(Rn)
......................... 59
3.3
Embeddings
............................. 70
3.4
Extensions
.............................. 72
3.5
Traces
................................ 79
3.6
Notes
................................ 82
4
Sobolev spaces on domains
87
4.1
Basic definitions
........................... 87
4.2
Extensions and intrinsic norms
................... 88
4.3
Odd and even extensions
...................... 94
4.4
Periodic representations and compact embeddings
......... 97
4.5
Traces
................................ 103
4.6
Notes
................................ 112
viii Contents
5
Elliptic
operators
in
L
2 117
5.1
Boundary value problems
...................... 117
5.2
Outline of the programme, and some basic ideas
.......... 120
5.3
A priori estimates
.......................... 122
5.4
Some properties of Sobolev spaces on R^.
............. 130
5.5
TheLaplacian
............................ 135
5.6
Homogeneous boundary value problems
.............. 145
5.7
Inhomogeneous boundary value problems
............. 151
5.8
Smoothness theory
......................... 154
5.9
The classical theory
......................... 160
5.10
Green s functions and Sobolev embeddings
............ 164
5.11
Degenerate elliptic operators
.................... 168
5.12
Notes
................................ 170
6
Spectral theory in
Hubert
spaces and Banach spaces
182
6.1
Introduction and examples
..................... 182
6.2
Spectral theory of self-adjoint operators
.............. 187
6.3
Approximation numbers and entropy numbers
:
definition and basic
properties
.............................. 190
6.4
Approximation numbers and entropy numbers: spectral assertions
194
6.5
The negative spectrum
....................... 200
6.6
Associated eigenelements
...................... 205
6.7
Notes
................................ 206
7
Compact embeddings, spectral theory of elliptic operators
214
7.1
Introduction
............................. 214
7.2
Compact embeddings: sequence spaces
.............. 215
7.3
Compact embeddings: function spaces
............... 221
7.4
Spectral theory of elliptic operators: the self-adjoint case
..... 227
7.5
Spectral theory of elliptic operators: the regular case
....... 229
7.6
Spectral theory of elliptic operators: the degenerate case
..... 232
7.7
The negative spectram
....................... 234
7.8
Notes
................................ 238
Â
Domains, basic spaces, and integral formulae
245
A.
1
Basic notation and basic spaces
................... 245
A.2 Domains
............................... 246
A.3 Integral formulae
.......................... 247
A.4 Surface area
............................. 248
8
Orthonormal
bases of trigonometric functions
250
Contents ix
С
Operator
theory
252
C.I Operators
in Banach
spaces
..................... 252
C.2 Symmetric and self-adjoint operators in Hilbert spaces
...... 254
C.3 Semi-bounded and positive-definite operators in Hilbert spaces
. . 256
D
Some integral inequalities
259
E
Function spaces
261
E.I Definitions, basic properties
.................... 261
E.2 Special cases, equivalent norms
................... 264
Selected solutions
269
Bibliography
275
Author index
283
List of figures
285
Notation index
286
Subject index
290
|
| adam_txt |
Contents
Preface
v
1
The Laplace-Poisson equation
1
1.1
Introduction, basic definitions, and plan of the book
. 1
1.2
Fundamental solutions and integral representations
. 3
1.3
Green's functions
. 6
1.4
Harmonic functions
. 10
1.5
The Dirichlet problem
. 17
1.6
The
Poisson
equation
. 20
1.7
Notes
. 23
2
Distributions
25
2.1
The spaces
£>(Ω)
and
£>'(Ώ)
. 25
2.2
Regular distributions, further examples
. 27
2.3
Derivatives and multiplications with smooth functions
. 31
2.4
Localisations, the spaces
6'(Ω)
. 33
2.5
The space
-8(Џ"),
the Fourier transform
. 38
2.6
The space
Ѕ'(Џп)
. 43
2.7
The Fourier transform in
£'(№."). 47
2.8
The Fourier transform in LpflR")
. 49
2.9
Notes
. 53
3
Sobolev spaces on R" and R^.
56
3.1
The spaces w£(Rn)
. 56
3.2
The spaces Hs(Rn)
. 59
3.3
Embeddings
. 70
3.4
Extensions
. 72
3.5
Traces
. 79
3.6
Notes
. 82
4
Sobolev spaces on domains
87
4.1
Basic definitions
. 87
4.2
Extensions and intrinsic norms
. 88
4.3
Odd and even extensions
. 94
4.4
Periodic representations and compact embeddings
. 97
4.5
Traces
. 103
4.6
Notes
. 112
viii Contents
5
Elliptic
operators
in
L
2 117
5.1
Boundary value problems
. 117
5.2
Outline of the programme, and some basic ideas
. 120
5.3
A priori estimates
. 122
5.4
Some properties of Sobolev spaces on R^.
. 130
5.5
TheLaplacian
. 135
5.6
Homogeneous boundary value problems
. 145
5.7
Inhomogeneous boundary value problems
. 151
5.8
Smoothness theory
. 154
5.9
The classical theory
. 160
5.10
Green's functions and Sobolev embeddings
. 164
5.11
Degenerate elliptic operators
. 168
5.12
Notes
. 170
6
Spectral theory in
Hubert
spaces and Banach spaces
182
6.1
Introduction and examples
. 182
6.2
Spectral theory of self-adjoint operators
. 187
6.3
Approximation numbers and entropy numbers
:
definition and basic
properties
. 190
6.4
Approximation numbers and entropy numbers: spectral assertions
194
6.5
The negative spectrum
. 200
6.6
Associated eigenelements
. 205
6.7
Notes
. 206
7
Compact embeddings, spectral theory of elliptic operators
214
7.1
Introduction
. 214
7.2
Compact embeddings: sequence spaces
. 215
7.3
Compact embeddings: function spaces
. 221
7.4
Spectral theory of elliptic operators: the self-adjoint case
. 227
7.5
Spectral theory of elliptic operators: the regular case
. 229
7.6
Spectral theory of elliptic operators: the degenerate case
. 232
7.7
The negative spectram
. 234
7.8
Notes
. 238
Â
Domains, basic spaces, and integral formulae
245
A.
1
Basic notation and basic spaces
. 245
A.2 Domains
. 246
A.3 Integral formulae
. 247
A.4 Surface area
. 248
8
Orthonormal
bases of trigonometric functions
250
Contents ix
С
Operator
theory
252
C.I Operators
in Banach
spaces
. 252
C.2 Symmetric and self-adjoint operators in Hilbert spaces
. 254
C.3 Semi-bounded and positive-definite operators in Hilbert spaces
. . 256
D
Some integral inequalities
259
E
Function spaces
261
E.I Definitions, basic properties
. 261
E.2 Special cases, equivalent norms
. 264
Selected solutions
269
Bibliography
275
Author index
283
List of figures
285
Notation index
286
Subject index
290 |
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| id | DE-604.BV023338791 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:00:50Z |
| indexdate | 2024-07-09T21:16:18Z |
| institution | BVB |
| isbn | 9783037190425 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016522606 |
| oclc_num | 254092397 |
| open_access_boolean | |
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| physical | IX, 294 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | European Math. Soc. |
| record_format | marc |
| series2 | EMS textbooks in mathematics |
| spelling | Haroske, Dorothee 1968- Verfasser (DE-588)118052489 aut Distributions, Sobolev spaces, elliptic equations Dorothee D. Haroske ; Hans Triebel Zürich European Math. Soc. 2008 IX, 294 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier EMS textbooks in mathematics Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 s Sobolev-Raum (DE-588)4055345-0 s Elliptische Differentialgleichung (DE-588)4014485-9 s DE-604 Triebel, Hans 1936- Verfasser (DE-588)133515923 aut Erscheint auch als Haroske, Dorothee, 1968- Distributions, Sobolev spaces, elliptic equations Online-Ausgabe 978-3-03719-542-0 (DE-604)BV036713224 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016522606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Haroske, Dorothee 1968- Triebel, Hans 1936- Distributions, Sobolev spaces, elliptic equations Sobolev-Raum (DE-588)4055345-0 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd |
| subject_GND | (DE-588)4055345-0 (DE-588)4014485-9 (DE-588)4070505-5 |
| title | Distributions, Sobolev spaces, elliptic equations |
| title_auth | Distributions, Sobolev spaces, elliptic equations |
| title_exact_search | Distributions, Sobolev spaces, elliptic equations |
| title_exact_search_txtP | Distributions, Sobolev spaces, elliptic equations |
| title_full | Distributions, Sobolev spaces, elliptic equations Dorothee D. Haroske ; Hans Triebel |
| title_fullStr | Distributions, Sobolev spaces, elliptic equations Dorothee D. Haroske ; Hans Triebel |
| title_full_unstemmed | Distributions, Sobolev spaces, elliptic equations Dorothee D. Haroske ; Hans Triebel |
| title_short | Distributions, Sobolev spaces, elliptic equations |
| title_sort | distributions sobolev spaces elliptic equations |
| topic | Sobolev-Raum (DE-588)4055345-0 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd |
| topic_facet | Sobolev-Raum Elliptische Differentialgleichung Distribution Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016522606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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