Singularities of solutions of second order quasilinear equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Edinburgh [u.a.]
Longman
1996
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Pitman research notes in mathematics series
353 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 377 S. |
| ISBN: | 0582035392 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010943634 | ||
| 003 | DE-604 | ||
| 005 | 20131031 | ||
| 007 | t | ||
| 008 | 960911s1996 |||| 00||| eng d | ||
| 020 | |a 0582035392 |9 0-582-03539-2 | ||
| 035 | |a (OCoLC)645625195 | ||
| 035 | |a (DE-599)BVBBV010943634 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-12 |a DE-29T |a DE-20 |a DE-11 |a DE-188 | ||
| 084 | |a SI 880 |0 (DE-625)143209: |2 rvk | ||
| 084 | |a SK 560 |0 (DE-625)143246: |2 rvk | ||
| 100 | 1 | |a Véron, Laurent |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Singularities of solutions of second order quasilinear equations |c Laurent Véron |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Edinburgh [u.a.] |b Longman |c 1996 | |
| 300 | |a 377 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman research notes in mathematics series |v 353 | |
| 650 | 0 | 7 | |a Nichtlineare parabolische Differentialgleichung |0 (DE-588)4455524-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Singuläre Lösung |0 (DE-588)4290969-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare elliptische Differentialgleichung |0 (DE-588)4310554-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare elliptische Differentialgleichung |0 (DE-588)4310554-3 |D s |
| 689 | 0 | 1 | |a Singuläre Lösung |0 (DE-588)4290969-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Nichtlineare parabolische Differentialgleichung |0 (DE-588)4455524-6 |D s |
| 689 | 1 | 1 | |a Singuläre Lösung |0 (DE-588)4290969-7 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Pitman research notes in mathematics series |v 353 |w (DE-604)BV000022845 |9 353 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007318710 | ||
Datensatz im Suchindex
| _version_ | 1804125430421127168 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Véron, Laurent |
| author_facet | Véron, Laurent |
| author_role | aut |
| author_sort | Véron, Laurent |
| author_variant | l v lv |
| building | Verbundindex |
| bvnumber | BV010943634 |
| classification_rvk | SI 880 SK 560 |
| ctrlnum | (OCoLC)645625195 (DE-599)BVBBV010943634 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01866nam a2200433 cb4500</leader><controlfield tag="001">BV010943634</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20131031 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960911s1996 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0582035392</subfield><subfield code="9">0-582-03539-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)645625195</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010943634</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 880</subfield><subfield code="0">(DE-625)143209:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 560</subfield><subfield code="0">(DE-625)143246:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Véron, Laurent</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Singularities of solutions of second order quasilinear equations</subfield><subfield code="c">Laurent Véron</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Edinburgh [u.a.]</subfield><subfield code="b">Longman</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">377 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Pitman research notes in mathematics series</subfield><subfield code="v">353</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare parabolische Differentialgleichung</subfield><subfield code="0">(DE-588)4455524-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Singuläre Lösung</subfield><subfield code="0">(DE-588)4290969-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare elliptische Differentialgleichung</subfield><subfield code="0">(DE-588)4310554-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare elliptische Differentialgleichung</subfield><subfield code="0">(DE-588)4310554-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Singuläre Lösung</subfield><subfield code="0">(DE-588)4290969-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Nichtlineare parabolische Differentialgleichung</subfield><subfield code="0">(DE-588)4455524-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Singuläre Lösung</subfield><subfield code="0">(DE-588)4290969-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Pitman research notes in mathematics series</subfield><subfield code="v">353</subfield><subfield code="w">(DE-604)BV000022845</subfield><subfield code="9">353</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007318710</subfield></datafield></record></collection> |
| 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 |
| open_access_boolean | |
| owner | DE-739 DE-12 DE-29T DE-20 DE-11 DE-188 |
| owner_facet | DE-739 DE-12 DE-29T DE-20 DE-11 DE-188 |
| 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 |