Singularities of solutions of second order quasilinear equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Edinburgh [u.a.]
Longman
1996
|
| Edition: | 1. publ. |
| Series: | Pitman research notes in mathematics series
353 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 377 S. |
| ISBN: | 0582035392 |
Staff View
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| 100 | 1 | |a Véron, Laurent |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Singularities of solutions of second order quasilinear equations |c Laurent Véron |
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| 264 | 1 | |a Edinburgh [u.a.] |b Longman |c 1996 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 1
1 Singularities of linear and quasilinear elliptic equations
1 1 Linear equations 6
1 1 1 Some basic notations in Riemannian geometry 6
1 1 2 Spherical harmonics 8
1 1 3 Sobolev spaces and capacities 9
1 1 4 Linear equations in non divergence form 11
1 1 5 Linear equations in divergence form 18
1 2 Quasilinear equations in divergence form 22
1 2 1 General framework for quasilinear equations 22
1 2 2 Removable singularities 25
1 2 3 Equations of mean curvature type 33
1 2 4 Characterization of isolated singularities 35
2 Singularities of solutions of elliptic equations with absorption
term
2 1 Isolated singularities 46
2 1 1 Isotropic singularities for solutions of equations 46
2 1 2 Strong singularities for solutions of Au + lu^ 1 u = 0 56
2 1 3 Weak singularities for solutions of 4u + |u|q~ u = 0 66
2 1 4 Existence of singular solutions 77
2 1 5 Prescribed singular submanifolds 83
2 2 Removable singularities 88
2 2 1 Removable isolated singularities 88
2 2 2 Removable singularities for positive solutions 93
2 2 3 General removable singularities 97
2 2 4 Elliptic operators with discontinuous coefficients 104
3 Singularities of solutions of elliptic equations with source term
3 1 Isolated singularities in differential inequalities 107
3 1 1 The Brezis Lions Lemma 107
3 1 2 Isotropic singularities of differential inequalities 112
3 2 Isolated singularities of solutions of Au±g(u) = 0 119
3 2 1 Symmetry properties of positive singular solutions 119
3 2 2 Isolated singularities of solutions of Au = g(u) 122
3 2 3 Isolated singularities of solutions of Au = g(u) 125
3 3 Singularities of solutions of Au = uq 135
3 3 1 The case l q N/(N 2) 135
3 3 2 The a priori estimate 136
3 3 3 Equations on compact Riemannian manifolds 141
3 3 4 The convergence theorems 149
3 3 5 Prescribed singularities 161
3 3 6 The asymptotic symmetry method 168
4 Boundary singularities of solutions of elliptic equations
4 1 Equations with absorption term 175
4 1 1 The model example 175
4 1 2 Measure boundary data 176
4 1 3 Removable singularities: the smooth case 188
4 1 4 More on removable singularities 198
4 1 5 Strong singularities 207
4 1 6 Weak singularities 214
4 2 Solutions with boundary blow up 217
4 2 1 Uniform boundary blow up: the smooth case 217
4 2 2 Uniform boundary blow up: the irregular case 224
4 3 Boundary trace of positive solutions 228
4 3 1 The global trace result 228
4 3 2 The local trace result and the trace elements 233
5 Singularities of quasilinear elliptic equations involving the p
Laplace or the mean curvature operator
5 1 The p Laplace equation 242
5 1 1 C ^ regularity results for degenerate elliptic equations 242
5 1 2 Singular p harmonic functions 243
5 2 Equations with absorption term 255
5 2 1 Removability results 255
5 2 2 The singular Dirichlet problem 259
5 2 3 Classification of non negative singularities 268
5 2 4 Global solutions 275
5 3 Equations with source term 277
5 3 1 The Bidaut Veron Lemma 277
5 3 2 Isolated singularities in the sub critical case 284
5 3 3 Isolated singularities in the super critical case 289
5 4 Singular solutions of the capillarity equations 294
5 4 1 Existence results 294
5 4 2 Global existence and uniqueness results 297
5 4 3 Further extensions 299
6 Singularities of nonlinear parabolic equations
6 1 Singularities of linear or quasilinear equations 301
6 1 1 The heat equation 301
6 1 2 Removable singularities for parabolic equations 302
6 1 3 Isolated singularities for parabolic equations 305
6 1 4 The Aronson and Serrin s results 310
6 2 Isolated Singularities the absorption case 313
6 2 1 Removable singularities 313
6 2 2 Measure as initial data 319
6 2 3 The very singular solutions 322
6 2 4 Strong singularities 328
6 2 5 Weak singularities 337
6 2 6 Miscellaneous 343
6 3 Isolated singularities the source case 344
6 3 1 Singularities of solutions of parabolic inequalities 344
6 3 2 Isolated singularities of source type equations 351
6 3 3 Rapidly decaying solutions 355
6.4. Some quasilinear equations 357
6 4 1 The porous media and the p Laplacian flows 357
6 4 2 The porous media equation with absoption 358
6 4 3 The p Laplacian evolution equation with absorption 363
References 365
|
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| id | DE-604.BV010943634 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:01:26Z |
| institution | BVB |
| isbn | 0582035392 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007318710 |
| oclc_num | 645625195 |
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| physical | 377 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Longman |
| record_format | marc |
| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Véron, Laurent Verfasser aut Singularities of solutions of second order quasilinear equations Laurent Véron 1. publ. Edinburgh [u.a.] Longman 1996 377 S. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 353 Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd rswk-swf Singuläre Lösung (DE-588)4290969-7 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 s Singuläre Lösung (DE-588)4290969-7 s DE-604 Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 s Pitman research notes in mathematics series 353 (DE-604)BV000022845 353 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007318710&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Véron, Laurent Singularities of solutions of second order quasilinear equations Pitman research notes in mathematics series Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd Singuläre Lösung (DE-588)4290969-7 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| subject_GND | (DE-588)4455524-6 (DE-588)4290969-7 (DE-588)4310554-3 |
| title | Singularities of solutions of second order quasilinear equations |
| title_auth | Singularities of solutions of second order quasilinear equations |
| title_exact_search | Singularities of solutions of second order quasilinear equations |
| title_full | Singularities of solutions of second order quasilinear equations Laurent Véron |
| title_fullStr | Singularities of solutions of second order quasilinear equations Laurent Véron |
| title_full_unstemmed | Singularities of solutions of second order quasilinear equations Laurent Véron |
| title_short | Singularities of solutions of second order quasilinear equations |
| title_sort | singularities of solutions of second order quasilinear equations |
| topic | Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd Singuläre Lösung (DE-588)4290969-7 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| topic_facet | Nichtlineare parabolische Differentialgleichung Singuläre Lösung Nichtlineare elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007318710&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022845 |
| work_keys_str_mv | AT veronlaurent singularitiesofsolutionsofsecondorderquasilinearequations |