Fine regularity of solutions of elliptic partial differential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1997]
|
| Series: | Mathematical surveys and monographs
Volume 51 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007918636&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | xiv, 291 Seiten |
| ISBN: | 0821803352 9780821803356 |
Staff View
MARC
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| 245 | 1 | 0 | |a Fine regularity of solutions of elliptic partial differential equations |c Jan Malý ; William P. Ziemer |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1997] | |
| 264 | 4 | |c © 1997 | |
| 300 | |a xiv, 291 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v Volume 51 | |
| 650 | 7 | |a EDP elliptique |2 inriac | |
| 650 | 7 | |a Equations différentielles elliptiques - Solutions numériques |2 ram | |
| 650 | 7 | |a Potentiel, Théorie du |2 ram | |
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| 650 | 7 | |a capacité |2 inriac | |
| 650 | 7 | |a espace Sobolev |2 inriac | |
| 650 | 7 | |a inégalité variationnelle |2 inriac | |
| 650 | 7 | |a problème valeur limite |2 inriac | |
| 650 | 7 | |a régularité |2 inriac | |
| 650 | 7 | |a théorie potentiel |2 inriac | |
| 650 | 7 | |a équation quasi linéaire |2 inriac | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Differential equations, Elliptic |x Numerical solutions | |
| 650 | 4 | |a Potential theory (Mathematics) | |
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Record in the Search Index
| _version_ | 1819308071621492736 |
|---|---|
| adam_text | Contents
Preface ix
Basic Notation xiii
Chapter 1. Preliminaries 1
1.1 Basic results 1
1.1.1 Covering theorems 7
1.1.2 Densities of measures 9
1.1.3 The maximal function and its applications 11
1.2 Potential estimates 14
1.3 Sobolev spaces 21
1.3.1 Inequalities 28
1.3.2 Imbeddings 31
1.3.3 Pointwise differentiability of Sobolev functions 40
1.3.4 Spaces Y1* 45
1.3.5 Adams inequality 50
1.3.6 Bessel and Riesz potentials 57
1.4 Historical notes 61
Chapter 2. Potential Theory 63
2.1 Capacity 63
2.1.1 Comparison of capacities; capacities of balls 66
2.1.2 Polar sets 71
2.1.3 Quasicontinuity 73
2.1.4 Multipliers 77
2.1.5 Capacity and energy minimizers 78
2.1.6 Thinness 84
2.1.7 Capacity and Hausdorff measure 86
2.1.8 Lebesgue points for Sobolev functions 89
2.2 Laplace equation 92
2.2.1 Green potentials 98
2.2.2 Classical thinness 102
2.2.3 Dirichlet problem and the Wiener criterion 105
2.3 Regularity of minimizers 109
2.3.1 Abstract minimization 110
2.3.2 Minimizers and weak solutions 110
2.3.3 Higher regularity 115
2.3.4 The De Giorgi method 118
2.3.5 Moser s iteration technique 122
vii
viii CONTENTS
2.3.6 Removable singularities 126
2.3.7 Estimates of supersolutions 128
2.3.8 Estimates of energy minimizers 131
2.3.9 Dirichlet problem 135
2.3.10 Application of thinness: the Wiener criterion 139
2.4 Fine topology 143
2.5 Fine Sobolev spaces 148
2.6 Historical notes 157
Chapter 3. Quasilinear Equations 161
3.1 Basic properties of weak solutions 161
3.1.1 Upper bounds for weak solutions 167
3.1.2 Weak Harnack inequality 174
3.1.3 Removable sets for weak solutions 178
3.2 Higher regularity of equations with differentiable structure 180
3.3 Historical notes 182
Chapter 4. Fine Regularity Theory 185
4.1 Basic energy estimates 185
4.2 Sufficiency of the Wiener condition for boundary regularity 197
4.2.1 The special case of harmonic functions 204
4.3 Necessity of the Wiener condition for boundary regularity 210
4.3.1 Main estimate 211
4.3.2 Necessity of the Wiener condition 224
4.4 Equations with measure data 225
4.5 Historical notes 230
Chapter 5. Variational Inequalities Regularity 233
5.1 Differential operators with measurable coefficients 233
5.1.1 Continuity in the presence of irregular obstacles 234
5.1.2 The modulus of continuity 236
5.2 Differential operators with differentiable structure 238
5.3 Historical notes 251
Chapter 6. Existence Theory 253
6.1 Existence of solutions to variational inequalities 253
6.1.1 Pseudomonotone operators 262
6.1.2 Variational problems existence of bounded solutions 263
6.1.3 Variational problems leading to unbounded solutions 266
6.2 The Dirichlet problem for equations with differentiable structure 269
6.3 Historical notes 270
References 273
Index 283
Notation Index 289
|
| any_adam_object | 1 |
| author | Malý, Jan 1955- Ziemer, William P. 1934-2017 |
| author_GND | (DE-588)1051223741 (DE-588)172473683 |
| author_facet | Malý, Jan 1955- Ziemer, William P. 1934-2017 |
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| author_sort | Malý, Jan 1955- |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011738453 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:17:48Z |
| institution | BVB |
| isbn | 0821803352 9780821803356 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007918636 |
| oclc_num | 36761648 |
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| physical | xiv, 291 Seiten |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Malý, Jan 1955- Ziemer, William P. 1934-2017 Fine regularity of solutions of elliptic partial differential equations Mathematical surveys and monographs EDP elliptique inriac Equations différentielles elliptiques - Solutions numériques ram Potentiel, Théorie du ram Problèmes aux limites ram capacité inriac espace Sobolev inriac inégalité variationnelle inriac problème valeur limite inriac régularité inriac théorie potentiel inriac équation quasi linéaire inriac Boundary value problems Differential equations, Elliptic Numerical solutions Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4046939-6 (DE-588)4014485-9 (DE-588)4048395-2 |
| title | Fine regularity of solutions of elliptic partial differential equations |
| title_auth | Fine regularity of solutions of elliptic partial differential equations |
| title_exact_search | Fine regularity of solutions of elliptic partial differential equations |
| title_full | Fine regularity of solutions of elliptic partial differential equations Jan Malý ; William P. Ziemer |
| title_fullStr | Fine regularity of solutions of elliptic partial differential equations Jan Malý ; William P. Ziemer |
| title_full_unstemmed | Fine regularity of solutions of elliptic partial differential equations Jan Malý ; William P. Ziemer |
| title_short | Fine regularity of solutions of elliptic partial differential equations |
| title_sort | fine regularity of solutions of elliptic partial differential equations |
| topic | EDP elliptique inriac Equations différentielles elliptiques - Solutions numériques ram Potentiel, Théorie du ram Problèmes aux limites ram capacité inriac espace Sobolev inriac inégalité variationnelle inriac problème valeur limite inriac régularité inriac théorie potentiel inriac équation quasi linéaire inriac Boundary value problems Differential equations, Elliptic Numerical solutions Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | EDP elliptique Equations différentielles elliptiques - Solutions numériques Potentiel, Théorie du Problèmes aux limites capacité espace Sobolev inégalité variationnelle problème valeur limite régularité théorie potentiel équation quasi linéaire Boundary value problems Differential equations, Elliptic Numerical solutions Potential theory (Mathematics) Potenzialtheorie Elliptische Differentialgleichung Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007918636&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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