Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
de Gruyter
1996
|
| Schriftenreihe: | De Gruyter series in nonlinear analysis and applications
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 547 S. graph. Darst. |
| ISBN: | 3110151138 |
Internformat
MARC
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| 020 | |a 3110151138 |c Gb. |9 3-11-015113-8 | ||
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| 035 | |a (DE-599)BVBBV010903748 | ||
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| 084 | |a MAT 464f |2 stub | ||
| 100 | 1 | |a Runst, Thomas |d 1952- |e Verfasser |0 (DE-588)109952596 |4 aut | |
| 245 | 1 | 0 | |a Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations |c Thomas Runst ; Winfried Sickel |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 1996 | |
| 300 | |a X, 547 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter series in nonlinear analysis and applications |v 3 | |
| 650 | 7 | |a Equations différentielles elliptiques |2 ram | |
| 650 | 7 | |a Equações diferenciais parciais eliticas |2 larpcal | |
| 650 | 7 | |a Espaços de sobolev |2 larpcal | |
| 650 | 7 | |a Problemas de contorno |2 larpcal | |
| 650 | 7 | |a Problèmes aux limites |2 ram | |
| 650 | 7 | |a Sobolev, Espaces de |2 ram | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Differential equations, Elliptic | |
| 650 | 4 | |a Sobolev spaces | |
| 650 | 0 | 7 | |a Elliptisches Randwertproblem |0 (DE-588)4193399-0 |2 gnd |9 rswk-swf |
| 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 Nichtlineares Randwertproblem |0 (DE-588)4129830-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionenraum |0 (DE-588)4134834-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Sobolev-Raum |0 (DE-588)4055345-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nemytskij-Operator |0 (DE-588)4427038-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elliptisches Randwertproblem |0 (DE-588)4193399-0 |D s |
| 689 | 0 | 1 | |a Nichtlineares Randwertproblem |0 (DE-588)4129830-5 |D s |
| 689 | 0 | 2 | |a Funktionenraum |0 (DE-588)4134834-5 |D s |
| 689 | 0 | 3 | |a Sobolev-Raum |0 (DE-588)4055345-0 |D s |
| 689 | 0 | 4 | |a Nemytskij-Operator |0 (DE-588)4427038-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Sobolev-Raum |0 (DE-588)4055345-0 |D s |
| 689 | 1 | 1 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
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| 689 | 3 | |5 DE-604 | |
| 689 | 4 | 0 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |D s |
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| 700 | 1 | |a Sickel, Winfried |d 1954- |e Verfasser |0 (DE-588)110590813 |4 aut | |
| 830 | 0 | |a De Gruyter series in nonlinear analysis and applications |v 3 |w (DE-604)BV005530011 |9 3 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-007293027 | ||
Datensatz im Suchindex
| _version_ | 1804125395294879744 |
|---|---|
| adam_text | Contents
1
Introduction
1
2
Function spaces of Besov-Triebel-Lizorkin type
5
2.1
Definitions and fundamental properties
............... 5
2.1.1
Definitions
......................... 5
2.1.2
Classical function spaces and their appearance in the scales
p,qpq
2.1.3
Basic properties
...................... . 14
2.1.4
Lifting property and related quasi-norms
......... 18
2.1.5
Dual spaces
......................... 19
2.1.6
Supplements: Fourier multiplies and maximal inequalities
. 21
2.2
Embeddings
............................. 29
2.2.1
Elementary embeddings
................... 29
2.2.2
Embeddings with constant smoothness
........... 30
2.2.3
Embeddings with constant differential dimension
..... 31
2.2.4
Embeddings in
Lœ,
Цос
and Lp
.............. 32
2.2.5
Embeddings for spaces of bounded functions
....... 37
2.3
Some equivalent characterizations of Fpq and Bpq
......... 41
2.3.1
Characterizations by differences and some representatives
of Fp q and Bsptq
....................... 41
2.3.2
Nikol skij representations
.................. 58
2.3.3
Wavelets and atoms
..................... 62
2.3.4
A localization property and Fubini-type theorems
..... 69
2.4
Spaces on domains
......................... 72
2.4.1
Preliminaries and definition
................. 72
2.4.2
Traces and extensions
.................... 75
2.4.3
An appropriate lifting operator
............... 76
2.4.4
Embeddings, density and duality
.............. 81
2.4.5
Intrinsic characterizations
.................. 84
2.5
Interpolation
............................. 85
2.5.1
The real method
....................... 86
2.5.2
The complex method
.................... 86
2.5.3
The i-method of Gustaffson-Peetre
............ 87
2.5.4
Interpolation of nonlinear operators
............. 87
2.6
Homogeneous spaces and a further supplement
.......... 92
2.6.1
Definition
.......................... 93
2.6.2
Some basic properties
.................... 94
2.6.3
The spaces L£(r)(tsq) and ^(L^(r))
............. 95
Regular elliptic boundary value problems
99
3.1
Definitions and preliminaries
.................... 99
3.1.1
Introduction
......................... 99
3.1.2
Definitions
......................... 100
3.2
Estimates of integral operators
................... 102
3.2.1
A class of integral operators and its symbols
........ 102
3.2.2
Estimates of
К
in F£q and Bspq
.............. 105
3.2.3
Estimates of K. Non-homogeneous spaces
......... 110
3.3
Estimates of the
Poisson
integral
.................. 113
3.4
A priori estimates
.......................... 117
3.4.1
Liouville theorems
..................... 117
3.4.2
A priori estimates. Part
1:
Ж+,
constant coefficients
.... 119
3.4.3
A priori estimates. Part
2:
bounded
C°°-domains,
variable
coefficients
......................... 121
3.5
Regular elliptic boundary value problems
............. 124
3.5.1
Dual rich quasi-Banach spaces,
Fredholm
maps
...... 124
3.5.2
Homogeneous boundary conditions
............. 130
3.5.3
Non-homogeneous boundary conditions
.......... 135
3.5.4
Maximum principle
..................... 137
3.5.5
Counterexamples
...................... 139
Pointwise multiplication
142
4.1
Introduction
............................. 142
4.2
The definition of the product
.................... 143
4.2.1
The definition of the product in
У
............. 143
4.2.2
The definition of the product in
ű (ü)
........... 149
4.3
Necessary conditions for pointwise multiplication
......... 150
4.3.1
Necessary conditions in the general case
.......... 150
4.3.2
Necessary conditions in case
m
= 2............ 160
4.4
Products of a function and a distribution
.............. 163
4.4.1
A decomposition principle: paraproducts
.......... 163
4.4.2
Preliminaries. Basic estimates of the paraproducts
..... 165
4.4.3
Products of a distribution and a function. Part I
...... 171
4.4.4
Products of a distribution and a function. Part II
...... 176
4.5
Products of functions and a distribution. The general case
..... 181
4.5.1
Products in spaces with negative smoothness
....... 181
4.5.2
Products in spaces of positive smoothness
......... 187
4.6
The case of constant
ρ
....................... 190
4.6.1
General results
....................... 190
4.6.2
Products with a bounded factor
............... 197
4.6.3
Characteristic
functions as multipliers
...........207
4.6.4
Multiplication
algebras
...................221
4.7
The extremal case p —
ρ
and p2
=
oo
...............228
4.7.1
Multiplication with B^
..................229
4.7.2
Multiplication with F^q
..................230
4.8
Generalized Holder inequalities
...................232
4.8.1
Necessary conditions
....................232
4.8.2
Holder inequalities in case
s
> 0..............238
4.8.3
Holder inequalities in case
s
= 0..............240
4.9
The spaces A if and relations to
M
(Ap q)
............246
4.9.1
Embeddings for M(Fpsq)
.... ..............247
4.9.2
Embeddings for
M
(5^)..................252
4.9.3
A final remark to the definition of the product
....... 256
Nemytskij operators in spaces of Besov-Triebel-Lizorkin type
260
5.1
Introduction
............................. 260
5.2
Nemytskij operators in Lebesgue and
S
obolev
spaces
....... 261
5.2.1
Some preliminaries
..................... 261
5.2.2
Nemytskij operators in Lebesgue spaces
.......... 264
5.2.3
Nemytskij operators in Sobolev spaces Wp(O,)
....... 266
5.2.4
Composition operators on Sobolev spaces Wpm
....... 267
5.2.5
Composition operators on subspaces of Wpm
........ 278
5.3
The Composition operator corresponding to
а С
°°-function
G
in
%andZ£9
............................ 290
5.3.1
Necessary conditions
.................... 290
5.3.2
Powers of
ƒ......................... 312
5.3.3
Composition operators generated by smooth unbounded G.
Part I. Preliminaries
..................... 316
5.3.4
Composition operators generated by smooth unbounded G.
Part II. Bounded functions
................. 323
5.3.5
Composition operators generated by smooth unbounded G.
Part III. Unbounded functions
............... 326
5.3.6
Composition operators corresponding to
G
є
С00
(R)
... 334
5.3.7
Composition operators on Fp q
П
Fpsv and on Fp q
Π
L^ .
. 344
5.4
Powers of
ƒ............................. 350
5.4.1
The regularity of the absolute value of
ƒ ......... 350
5.4.2
Sublinear
functions
G
.................... 360
5.4.3
Fractional powers
/ μ,μ>1
............... 363
5.4.4
Fractional powers
/ μ,μ<1
.............. . 365
5.5
Supplements
............................. 367
5.5.1
Rffl
->
R-functions
G
.................... 367
5.5.2
Continuity of composition operators
............ 372
χ
Contents
5.5.3
Differentiability of composition operators
......... 378
5.5.4
Nemytskij operators and pseudodifferential operators
. . . 383
6
Applications to
semilinear
elliptic boundary problems
393
6.1
Introduction
............................. 393
6.2
The admissibility of spaces of Besov-Triebel-Lizorkin type
.... 397
6.2.1
The
Brouwer
degree of a map
............... 397
6.2.2
The Leray-Schauder degree
................ 398
6.2.3
Topological degree in Bsp q and Fp q
............ 400
6.3
Nonlinear perturbations of linear in
vertible
operators
....... 412
6.3.1
An abstract result
...................... 412
6.3.2
Bounded nonlinearities
................... 414
6.3.3
Sublinear
nonlinearities
................... 416
6.3.4
Nonlinearities with linear growth
.............. 418
6.3.5 Superlinear
nonlinearities
.................. 419
6.4
Results of Landesman-Lazer type
................. 423
6.4.1
The Ljapunov-Schmidt method
............... 424
6.4.2
The alternative lemma
................... 425
6.4.3
Bounded nonlinearities
................... 428
6.4.4
Sublinear nonlinearities
................... 436
6.4.5
Boundary value problems whose nonlinearities are of linear
growth
............................ 439
6.5
Results of Kazdan-Warner type
................... 449
6.5.1
Abstract results
....................... 450
6.5.2
Applications to
semilinear
elliptic boundary value problems
454
6.5.3
Solvability of equations depending on a parameter
..... 460
6.6
Results of Ambrosetti-Prodi type
.................. 467
6.6.1
Inversion problems in quasi-Banach spaces
........ 469
6.6.2
Singularity theory in quasi-Banach spaces
......... 473
6.6.3
Applications to nonlinear ellipitic boundary value problems
487
6.6.4
Further multiplicity results
................. 513
Bibliography
525
Index
545
|
| any_adam_object | 1 |
| author | Runst, Thomas 1952- Sickel, Winfried 1954- |
| author_GND | (DE-588)109952596 (DE-588)110590813 |
| author_facet | Runst, Thomas 1952- Sickel, Winfried 1954- |
| author_role | aut aut |
| author_sort | Runst, Thomas 1952- |
| author_variant | t r tr w s ws |
| building | Verbundindex |
| bvnumber | BV010903748 |
| callnumber-first | Q - Science |
| callnumber-label | QA323 |
| callnumber-raw | QA323 |
| callnumber-search | QA323 |
| callnumber-sort | QA 3323 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 560 SK 620 SK 600 |
| classification_tum | MAT 464f |
| ctrlnum | (OCoLC)35095971 (DE-599)BVBBV010903748 |
| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010903748 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:00:53Z |
| institution | BVB |
| isbn | 3110151138 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007293027 |
| oclc_num | 35095971 |
| open_access_boolean | |
| owner | DE-20 DE-384 DE-12 DE-91G DE-BY-TUM DE-29T DE-824 DE-634 DE-739 DE-11 DE-188 DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-20 DE-384 DE-12 DE-91G DE-BY-TUM DE-29T DE-824 DE-634 DE-739 DE-11 DE-188 DE-355 DE-BY-UBR DE-83 |
| physical | X, 547 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter series in nonlinear analysis and applications |
| series2 | De Gruyter series in nonlinear analysis and applications |
| spelling | Runst, Thomas 1952- Verfasser (DE-588)109952596 aut Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations Thomas Runst ; Winfried Sickel Berlin [u.a.] de Gruyter 1996 X, 547 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter series in nonlinear analysis and applications 3 Equations différentielles elliptiques ram Equações diferenciais parciais eliticas larpcal Espaços de sobolev larpcal Problemas de contorno larpcal Problèmes aux limites ram Sobolev, Espaces de ram Boundary value problems Differential equations, Elliptic Sobolev spaces Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Nichtlineares Randwertproblem (DE-588)4129830-5 gnd rswk-swf Funktionenraum (DE-588)4134834-5 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Nemytskij-Operator (DE-588)4427038-0 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 s Nichtlineares Randwertproblem (DE-588)4129830-5 s Funktionenraum (DE-588)4134834-5 s Sobolev-Raum (DE-588)4055345-0 s Nemytskij-Operator (DE-588)4427038-0 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Randwertproblem (DE-588)4048395-2 s Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Elliptische Differentialgleichung (DE-588)4014485-9 s Sickel, Winfried 1954- Verfasser (DE-588)110590813 aut De Gruyter series in nonlinear analysis and applications 3 (DE-604)BV005530011 3 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007293027&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Runst, Thomas 1952- Sickel, Winfried 1954- Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations De Gruyter series in nonlinear analysis and applications Equations différentielles elliptiques ram Equações diferenciais parciais eliticas larpcal Espaços de sobolev larpcal Problemas de contorno larpcal Problèmes aux limites ram Sobolev, Espaces de ram Boundary value problems Differential equations, Elliptic Sobolev spaces Elliptisches Randwertproblem (DE-588)4193399-0 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Nichtlineares Randwertproblem (DE-588)4129830-5 gnd Funktionenraum (DE-588)4134834-5 gnd Sobolev-Raum (DE-588)4055345-0 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Nemytskij-Operator (DE-588)4427038-0 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4193399-0 (DE-588)4048395-2 (DE-588)4014485-9 (DE-588)4129830-5 (DE-588)4134834-5 (DE-588)4055345-0 (DE-588)4044779-0 (DE-588)4427038-0 (DE-588)4128900-6 |
| title | Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations |
| title_auth | Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations |
| title_exact_search | Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations |
| title_full | Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations Thomas Runst ; Winfried Sickel |
| title_fullStr | Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations Thomas Runst ; Winfried Sickel |
| title_full_unstemmed | Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations Thomas Runst ; Winfried Sickel |
| title_short | Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations |
| title_sort | sobolev spaces of fractional order nemytskij operators and nonlinear partial differential equations |
| topic | Equations différentielles elliptiques ram Equações diferenciais parciais eliticas larpcal Espaços de sobolev larpcal Problemas de contorno larpcal Problèmes aux limites ram Sobolev, Espaces de ram Boundary value problems Differential equations, Elliptic Sobolev spaces Elliptisches Randwertproblem (DE-588)4193399-0 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Nichtlineares Randwertproblem (DE-588)4129830-5 gnd Funktionenraum (DE-588)4134834-5 gnd Sobolev-Raum (DE-588)4055345-0 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Nemytskij-Operator (DE-588)4427038-0 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Equations différentielles elliptiques Equações diferenciais parciais eliticas Espaços de sobolev Problemas de contorno Problèmes aux limites Sobolev, Espaces de Boundary value problems Differential equations, Elliptic Sobolev spaces Elliptisches Randwertproblem Randwertproblem Elliptische Differentialgleichung Nichtlineares Randwertproblem Funktionenraum Sobolev-Raum Partielle Differentialgleichung Nemytskij-Operator Nichtlineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007293027&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530011 |
| work_keys_str_mv | AT runstthomas sobolevspacesoffractionalordernemytskijoperatorsandnonlinearpartialdifferentialequations AT sickelwinfried sobolevspacesoffractionalordernemytskijoperatorsandnonlinearpartialdifferentialequations |