Concentration compactness: functional-analytic grounds and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Imperial College Press
2007
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 264 S. |
| ISBN: | 1860946674 9781860946677 9781860946660 1860946666 |
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| adam_text | CONCENTRATION COMPACTNESS FUNCTIONAL-ANALYTIC GROUNDS AND APPLICATIONS
KYRILTINTAREV KARL-HEINZ FIESEIER UPPSALA UNIVERSITY, SWEDEN IMPERIAL
COLLEGE PRESS CONTENTS PREFACE V 1. FUNCTIONAL SPACES AND CONVERGENCE 1
1.1 DEFINITIONS AND EXAMPLES OF FUNCTIONAL SPACES 1 1.2 HOLDER
INEQUALITY. YOUNG INEQUALITY FOR CONVOLUTIONS .... 4 1.3 ARZELAE-ASCOLI
THEOREM 7 1.4 HUBERT SPACE 8 1.5 WEAK CONVERGENCE 13 1.6 LINEAR
OPERATORS IN HILBERT SPACE 16 1.7 DIFFERENTIABLE FUNCTIONALS 20 1.8
CONTINUOUS AND DIFFERENTIABLE FUNCTIONALS IN L P -SPACES ... 23 2.
SOBOLEV SPACES 29 2.1 WEAK DERIVATIVES. DEFINITION OF SOBOLEV SPACES 29
2.2 CHAIN RULE 32 2.3 COORDINATE TRANSFORMATIONS. TRACE DOMAINS AND
EXTENSION DOMAINS 34 2.4 FRIEDRICHS INEQUALITY 37 2.5 COMPACTNESS LEMMA
39 2.6 POINCARE INEQUALITY 41 2.7 SPACE V 1 2 (R N ). SOBOLEV, HARDY
AND NASH INEQUALITIES ... 43 2.8 SOBOLEV IMBEDDINGS 47 2.9 TRACE ON THE
BOUNDARY 51 2.10 DIFFERENTIABLE FUNCTIONALS IN SOBOLEV SPACES 56 2.11
SOBOLEV SPACES OF HIGHER ORDER 57 IX X CONCENTRATION COMPACTNESS 3. WEAK
CONVERGENCE DECOMPOSITION 59 3.1 -WEAK CONVERGENCE AND DISLOCATION
SPACES 60 3.2 D-WEAK CONVERGENCE IN I 2 WITH SHIFTS 61 3.3 WEAK
CONVERGENCE DECOMPOSITION 62 3.4 UNIQUENESS IN THE WEAK CONVERGENCE
DECOMPOSITION 68 3.5 D-FLASK SUBSPACES. D-WEAK COMPACTNESS 69 3.6 D-WEAK
CONVERGENCE WITH SHIFT OPERATORS IN R N 70 3.7 CONSTRAINED MINIMIZATION
75 3.8 COMPACTNESS IN THE PRESENCE OF SYMMETRIES 77 3.9 THE
CONCENTRATION COMPACTNESS ARGUMENT 79 3.10 BIBLIOGRAPHIC REMARKS 80 4.
CONCENTRATION COMPACTNESS WITH EUCLIDEAN SHIFTS 83 4.1 FLASK SETS 83 4.2
EXISTENCE OF SOBOLEV MINIMIZERS ON FLASK DOMAINS 89 4.3 RELLICH SETS AND
COMPACTNESS OF SOBOLEV IMBEDDINGS .... 90 4.4 CONCENTRATION COMPACTNESS
WITH SYMMETRY 91 4.5 CONCENTRATION COMPACTNESS AND THE FRIEDRICHS
INEQUALITY 92 4.6 SOLVABILITY IN NON-FLASK DOMAINS 95 4.7 CONVERGENCE BY
PENALTY AT INFINITY 98 4.8 MINIMIZERS WITH FINITE SYMMETRY 100 4.9
POSITIVE NON-EXTREMAL SOLUTIONS 102 4.10 BIBLIOGRAPHIC REMARKS 107 5.
CONCENTRATION COMPACTNESS WITH DILATIONS 109 5.1 SEMILINEAR ELLIPTIC
EQUATIONS WITH THE CRITICAL EXPONENT . . . 109 5.2 OSCILLATORY CRITICAL
NONLINEARITY AND THE MINIMIZER IN THE SOBOLEV INEQUALITY 116 5.3 THE
BREZIS-NIRENBERG PROBLEM 121 5.4 MINIMIZER FOR THE CRITICAL TRACE
INEQUALITY 126 5.5 A SINGULAR SUBCRITICAL PROBLEM 131 5.6 MINIMIZER FOR
THE HARDY-SOBOLEV-MAZ YA INEQUALITY .... 136 5.7 BIBLIOGRAPHIC REMARKS
137 6. MINIMAX PROBLEMS 141 6.1 THE MOUNTAIN PASS THEOREM 142 6.2
FUNCTIONALS FOR THE SEMILINEAR ELLIPTIC PROBLEMS 145 CONTENTS XI 6.3
CRITICAL POINTS OF THE MOUNTAIN PASS TYPE 149 6.4 MOUNTAIN PASS PROBLEMS
WITH THE CRITICAL EXPONENT 155 6.5 CRITICAL PROBLEM WITH PUNITIVE
ASYMPTOTIC VALUES 157 6.6 BIBLIOGRAPHIC REMARKS 159 7. DIFFERENTIABLE
MANIFOLDS 161 7.1 DIFFERENTIABLE MANIFOLDS 161 7.2 TANGENT VECTORS AND
VECTOR FIELDS 164 7.3 COTANGENT VECTORS AND 1-FORMS 170 7.4 TENSOR
FIELDS OF DEGREE 2 172 7.5 DIFFERENTIAL FORMS 175 8. RIEMANNIAN
MANIFOLDS AND LIE GROUPS 181 8.1 RIEMANNIAN MANIFOLDS 181 8.2 LIE GROUPS
189 8.3 THE EXPONENTIAL MAP 193 8.4 LIE GROUP ACTIONS 197 8.5
INTEGRATION 199 8.6 BIBLIOGRAPHIC REMARKS 201 9. SOBOLEV SPACES ON
MANIFOLDS AND SUBELLIPTIC PROBLEMS 203 9.1 SOBOLEV INEQUALITY ON
PERIODIC MANIFOLDS 203 9.2 MAGNETIC SOBOLEV SPACE 205 9.3 MAGNETIC
SHIFTS AND D-CONVERGENCE 206 9.4 SUBELLIPTIC MOLLIFIERS AND SOBOLEV
SPACES ON CARNOT GROUPS 210 9.5 COMPACTNESS OF SUBELLIPTIC SOBOLEV
IMBEDDINGS 217 9.6 SUBELLIPTIC FRIEDRICHS AND POINCARE INEQUALITIES 218
9.7 SUBELLIPTIC SOBOLEV INEQUALITY 221 9.8 CONCENTRATION COMPACTNESS ON
CARNOT GROUPS DUE TO SHIFTS 222 9.9 CONCENTRATION COMPACTNESS ON CARNOT
GROUPS DUE TO DILATIONS 224 9.10 BIBLIOGRAPHIC REMARKS 227 10. FURTHER
APPLICATIONS 231 10.1 DILATIONS ON THE SPHERE AND YAMABE PROBLEM 231
10.2 GLOBAL COMPACTNESS IN SPACES H M (R N ) AND T M 2 (R N ) . . 232
XII CONCENTRATION COMPACTNESS 10.3 MINIMIZER IN THE NASH INEQUALITY 236
10.4 A MINIMIZATION PROBLEM WITH NONLOCAL TERM 237 10.5 CONCENTRATION
COMPACTNESS WITH TOPOLOGICAL CHARGE 240 10.6 BIBLIOGRAPHIC REMARKS 244
APPENDIX A COVERING LEMMA 247 APPENDIX * REARRANGEMENT INEQUALITIES 249
APPENDIX * MAXIMUM PRINCIPLE 251 BIBLIOGRAPHY 253 INDEX 261
|
| adam_txt |
CONCENTRATION COMPACTNESS FUNCTIONAL-ANALYTIC GROUNDS AND APPLICATIONS
KYRILTINTAREV KARL-HEINZ FIESEIER UPPSALA UNIVERSITY, SWEDEN IMPERIAL
COLLEGE PRESS CONTENTS PREFACE V 1. FUNCTIONAL SPACES AND CONVERGENCE 1
1.1 DEFINITIONS AND EXAMPLES OF FUNCTIONAL SPACES 1 1.2 HOLDER
INEQUALITY. YOUNG INEQUALITY FOR CONVOLUTIONS . 4 1.3 ARZELAE-ASCOLI
THEOREM 7 1.4 HUBERT SPACE 8 1.5 WEAK CONVERGENCE 13 1.6 LINEAR
OPERATORS IN HILBERT SPACE 16 1.7 DIFFERENTIABLE FUNCTIONALS 20 1.8
CONTINUOUS AND DIFFERENTIABLE FUNCTIONALS IN L P -SPACES . 23 2.
SOBOLEV SPACES 29 2.1 WEAK DERIVATIVES. DEFINITION OF SOBOLEV SPACES 29
2.2 CHAIN RULE 32 2.3 COORDINATE TRANSFORMATIONS. TRACE DOMAINS AND
EXTENSION DOMAINS 34 2.4 FRIEDRICHS INEQUALITY 37 2.5 COMPACTNESS LEMMA
39 2.6 POINCARE INEQUALITY 41 2.7 SPACE V 1 ' 2 (R N ). SOBOLEV, HARDY
AND NASH INEQUALITIES . 43 2.8 SOBOLEV IMBEDDINGS 47 2.9 TRACE ON THE
BOUNDARY 51 2.10 DIFFERENTIABLE FUNCTIONALS IN SOBOLEV SPACES 56 2.11
SOBOLEV SPACES OF HIGHER ORDER 57 IX X CONCENTRATION COMPACTNESS 3. WEAK
CONVERGENCE DECOMPOSITION 59 3.1 -WEAK CONVERGENCE AND DISLOCATION
SPACES 60 3.2 D-WEAK CONVERGENCE IN I 2 WITH SHIFTS 61 3.3 WEAK
CONVERGENCE DECOMPOSITION 62 3.4 UNIQUENESS IN THE WEAK CONVERGENCE
DECOMPOSITION 68 3.5 D-FLASK SUBSPACES. D-WEAK COMPACTNESS 69 3.6 D-WEAK
CONVERGENCE WITH SHIFT OPERATORS IN R N 70 3.7 CONSTRAINED MINIMIZATION
75 3.8 COMPACTNESS IN THE PRESENCE OF SYMMETRIES 77 3.9 THE
CONCENTRATION COMPACTNESS ARGUMENT 79 3.10 BIBLIOGRAPHIC REMARKS 80 4.
CONCENTRATION COMPACTNESS WITH EUCLIDEAN SHIFTS 83 4.1 FLASK SETS 83 4.2
EXISTENCE OF SOBOLEV MINIMIZERS ON FLASK DOMAINS 89 4.3 RELLICH SETS AND
COMPACTNESS OF SOBOLEV IMBEDDINGS . 90 4.4 CONCENTRATION COMPACTNESS
WITH SYMMETRY 91 4.5 CONCENTRATION COMPACTNESS AND THE FRIEDRICHS
INEQUALITY 92 4.6 SOLVABILITY IN NON-FLASK DOMAINS 95 4.7 CONVERGENCE BY
PENALTY AT INFINITY 98 4.8 MINIMIZERS WITH FINITE SYMMETRY 100 4.9
POSITIVE NON-EXTREMAL SOLUTIONS 102 4.10 BIBLIOGRAPHIC REMARKS 107 5.
CONCENTRATION COMPACTNESS WITH DILATIONS 109 5.1 SEMILINEAR ELLIPTIC
EQUATIONS WITH THE CRITICAL EXPONENT . . . 109 5.2 OSCILLATORY CRITICAL
NONLINEARITY AND THE MINIMIZER IN THE SOBOLEV INEQUALITY 116 5.3 THE
BREZIS-NIRENBERG PROBLEM 121 5.4 MINIMIZER FOR THE CRITICAL TRACE
INEQUALITY 126 5.5 A SINGULAR SUBCRITICAL PROBLEM 131 5.6 MINIMIZER FOR
THE HARDY-SOBOLEV-MAZ'YA INEQUALITY . 136 5.7 BIBLIOGRAPHIC REMARKS
137 6. MINIMAX PROBLEMS 141 6.1 THE MOUNTAIN PASS THEOREM 142 6.2
FUNCTIONALS FOR THE SEMILINEAR ELLIPTIC PROBLEMS 145 CONTENTS XI 6.3
CRITICAL POINTS OF THE MOUNTAIN PASS TYPE 149 6.4 MOUNTAIN PASS PROBLEMS
WITH THE CRITICAL EXPONENT 155 6.5 CRITICAL PROBLEM WITH PUNITIVE
ASYMPTOTIC VALUES 157 6.6 BIBLIOGRAPHIC REMARKS 159 7. DIFFERENTIABLE
MANIFOLDS 161 7.1 DIFFERENTIABLE MANIFOLDS 161 7.2 TANGENT VECTORS AND
VECTOR FIELDS 164 7.3 COTANGENT VECTORS AND 1-FORMS 170 7.4 TENSOR
FIELDS OF DEGREE 2 172 7.5 DIFFERENTIAL FORMS 175 8. RIEMANNIAN
MANIFOLDS AND LIE GROUPS 181 8.1 RIEMANNIAN MANIFOLDS 181 8.2 LIE GROUPS
189 8.3 THE EXPONENTIAL MAP 193 8.4 LIE GROUP ACTIONS 197 8.5
INTEGRATION 199 8.6 BIBLIOGRAPHIC REMARKS 201 9. SOBOLEV SPACES ON
MANIFOLDS AND SUBELLIPTIC PROBLEMS 203 9.1 SOBOLEV INEQUALITY ON
PERIODIC MANIFOLDS 203 9.2 "MAGNETIC" SOBOLEV SPACE 205 9.3 MAGNETIC
SHIFTS AND D-CONVERGENCE 206 9.4 SUBELLIPTIC MOLLIFIERS AND SOBOLEV
SPACES ON CARNOT GROUPS 210 9.5 COMPACTNESS OF SUBELLIPTIC SOBOLEV
IMBEDDINGS 217 9.6 SUBELLIPTIC FRIEDRICHS AND POINCARE INEQUALITIES 218
9.7 SUBELLIPTIC SOBOLEV INEQUALITY 221 9.8 CONCENTRATION COMPACTNESS ON
CARNOT GROUPS DUE TO SHIFTS 222 9.9 CONCENTRATION COMPACTNESS ON CARNOT
GROUPS DUE TO DILATIONS 224 9.10 BIBLIOGRAPHIC REMARKS 227 10. FURTHER
APPLICATIONS 231 10.1 DILATIONS ON THE SPHERE AND YAMABE PROBLEM 231
10.2 GLOBAL COMPACTNESS IN SPACES H M (R N ) AND T M 2 (R N ) . . 232
XII CONCENTRATION COMPACTNESS 10.3 MINIMIZER IN THE NASH INEQUALITY 236
10.4 A MINIMIZATION PROBLEM WITH NONLOCAL TERM 237 10.5 CONCENTRATION
COMPACTNESS WITH TOPOLOGICAL CHARGE 240 10.6 BIBLIOGRAPHIC REMARKS 244
APPENDIX A COVERING LEMMA 247 APPENDIX * REARRANGEMENT INEQUALITIES 249
APPENDIX * MAXIMUM PRINCIPLE 251 BIBLIOGRAPHY 253 INDEX 261 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:52:54Z |
| indexdate | 2024-07-09T20:45:19Z |
| institution | BVB |
| isbn | 1860946674 9781860946677 9781860946660 1860946666 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015029535 |
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| physical | XII, 264 S. |
| publishDate | 2007 |
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| publisher | Imperial College Press |
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| spelling | Tintarev, Kyril Verfasser aut Concentration compactness functional-analytic grounds and applications Kyril Tintarev ; Karl-Heinz Fieseler London Imperial College Press 2007 XII, 264 S. txt rdacontent n rdamedia nc rdacarrier Functional analysis Funktionenraum (DE-588)4134834-5 gnd rswk-swf Konvergenz (DE-588)4032326-2 gnd rswk-swf Kompaktheit (DE-588)4456100-3 gnd rswk-swf Konvergenz (DE-588)4032326-2 s Funktionenraum (DE-588)4134834-5 s Kompaktheit (DE-588)4456100-3 s DE-604 Fieseler, Karl-Heinz Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015029535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tintarev, Kyril Fieseler, Karl-Heinz Concentration compactness functional-analytic grounds and applications Functional analysis Funktionenraum (DE-588)4134834-5 gnd Konvergenz (DE-588)4032326-2 gnd Kompaktheit (DE-588)4456100-3 gnd |
| subject_GND | (DE-588)4134834-5 (DE-588)4032326-2 (DE-588)4456100-3 |
| title | Concentration compactness functional-analytic grounds and applications |
| title_auth | Concentration compactness functional-analytic grounds and applications |
| title_exact_search | Concentration compactness functional-analytic grounds and applications |
| title_exact_search_txtP | Concentration compactness functional-analytic grounds and applications |
| title_full | Concentration compactness functional-analytic grounds and applications Kyril Tintarev ; Karl-Heinz Fieseler |
| title_fullStr | Concentration compactness functional-analytic grounds and applications Kyril Tintarev ; Karl-Heinz Fieseler |
| title_full_unstemmed | Concentration compactness functional-analytic grounds and applications Kyril Tintarev ; Karl-Heinz Fieseler |
| title_short | Concentration compactness |
| title_sort | concentration compactness functional analytic grounds and applications |
| title_sub | functional-analytic grounds and applications |
| topic | Functional analysis Funktionenraum (DE-588)4134834-5 gnd Konvergenz (DE-588)4032326-2 gnd Kompaktheit (DE-588)4456100-3 gnd |
| topic_facet | Functional analysis Funktionenraum Konvergenz Kompaktheit |
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