Regularity estimates for nonlinear elliptic and parabolic problems: Cetraro, Italy 2009
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| Other Authors: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2012
|
| Series: | Lecture notes in mathematics
2045 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XI, 247 S. graph. Darst. 24 cm |
| ISBN: | 9783642271441 3642271448 9783642271458 |
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MARC
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Record in the Search Index
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IMAGE 1
C O N T E N T S
APPLICATIONS O F B O U N D A R Y HARNACK INEQUALITIES FOR P H A R M O N
I C FUNCTIONS A N D R E L A T E D TOPICS 1
J. LEWIS 1 OUTLINE OF THE COURSE 1
1.1 ODE T O THE P LAPLACIAN 1
1.2 MY INTRODUCTION T O P HARMONIC FUNCTIONS 2
2 BASIC ESTIMATES FOR THE P LAPLACIAN 2
2.1 P HARMONIC FUNCTIONS IN NTA DOMAINS 4
2.2 THE P LAPLACIAN AND ELLIPTIC P D E 6
2.3 DEGENERATE ELLIPTIC EQUATIONS 7
3 P HARMONIC MEASURE 9
3.1 P HARMONIC MEASURE IN SIMPLY CONNECTED DOMAINS 15
3.2 PRELIMINARY REDUCTIONS FOR THEOREM 2.6 15
3.3 PROOF OF THEOREM 2.8 16
3.4 THE FINAL PROOF 19
3.5 P HARMONIC MEASURE IN SPACE 21
3.6 OPEN PROBLEMS FOR P HARMONIC MEASURE 22
4 BOUNDARY HARNACK INEQUALITIES AND THE MARTIN BOUNDARY PROBLEM FOR P
HARMONIC FUNCTIONS 23
4.1 HISTORY OF THEOREM 3.1 24
4.2 PROOF OF STEP 1 26
4.3 PROOF OF STEP 2 .' 27
4.4 PROOF OF STEP 3 30
4.5 PROOF OF STEP 4 AND THEOREM 3.1 33
4.6 MORE ON BOUNDARY HARNACK INEQUALITIES 37
4.7 THE MARTIN BOUNDARY PROBLEM 38
4.8 PROOF OF THEOREM 3.9 42
4.9 FURTHER REMARKS 46
HTTP://D-NB.INFO/1017147574
IMAGE 2
X CONTENTS
5 UNIQUENESS AND REGULARITY IN FREE BOUNDARY: INVERSE TYPE PROBLEMS 46
5.1 HISTORY OF THEOREM 4.1 46
5.2 PROOF OF THEOREM 4.1 49
5.3 FURTHER UNIQUENESS RESULTS 50
5.4 BOUNDARY REGULARITY OF P HARMONIC FUNCTIONS 51
5.5 PROOF OF THEOREM 4.3 52
5.6 PROOF OF THEOREM 4.4 55
5.7 PROOF OF THEOREM 4.5 57
5.8 REGULARITY IN A LIPSCHITZ FREE BOUNDARY PROBLEM 59
5.9 HISTORY OF THEOREM 4.11 60
5.10 PROOF OF THEOREM 4.11 60
5.11 ENLARGEMENT OF THE CONE OF MONOTONICITY IN THE INTERIOR 61
5.12 ENLARGEMENT OF THE CONE OF MONOTONICITY A T THE FREE BOUNDARY 61
5.13 AN APPLICATION OF THEOREM 4.11 63
5.14 PROOF OF (161) 65
5.15 CLOSING REMARKS 68
REFERENCES 69
REGULARITY O F SUPERSOLUTIONS 73
PETER LINDQVIST 1 INTRODUCTION 73
2 THE STATIONARY EQUATION 78
3 THE EVOLUTIONARY EQUATION 91
3.1 DEFINITIONS 92
3.2 BOUNDED SUPERSOLUTIONS 94
3.3 UNBOUNDED SUPERSOLUTIONS 102
3.4 REDUCTION T O ZERO BOUNDARY VALUES 109
4 WEAK SUPERSOLUTIONS ARE SEMICONTINUOUS I L L
5 THE EQUATION WITH MEASURE D A T A 122
6 POINTWISE BEHAVIOUR 123
6.1 THE STATIONARY EQUATION 123
6.2 THE EVOLUTIONARY EQUATION 125
REFERENCES 130
I N T R O D U C T I O N T O R A N D O M TUG-OF-WAR G A M E S A N D P D E
S 133
J U A N J. MANFREDI 1 INTRODUCTION 133
2 PROBABILITY BACKGROUND 133
3 T H E P-LAPLACIAN GAMBLING HOUSE 141
4 P-HARMONIOUS FUNCTIONS 144
5 DIRECTED TREES 147
6 EPILOGUE 150
REFERENCES 151
IMAGE 3
CONTENTS XI
T H E P R O B L E M S O F T H E OBSTACLE IN LOWER
D I M E N S I O N A N D FOR T H E FRACTIONAL LAPLACIAN 153
SANDRO SALSA 1 INTRODUCTION 153
2 THE ZERO OBSTACLE PROBLEM 160
2.1 SETTING OF THE PROBLEM 160
2.2 LIPSCHITZ CONTINUITY AND SEMICONVEXITY 162
2.3 LOCAL C 1 '" ESTIMATE 166
2.4 OPTIMAL REGULARITY FOR TANGENTIALLY CONVEX GLOBAL SOLUTIONS 170
2.5 ALMGREN'S FREQUENCY FORMULA 173
2.6 ASYMPTOTIC PROFILES AND OPTIMAL REGULARITY 177
2.7 LIPSCHITZ CONTINUITY OF THE FREE BOUNDARY A T STABLE POINTS 180
2.8 BOUNDARY HARNACK PRINCIPLES AND C 1 '" REGULARITY OF THE FREE
BOUNDARY A T STABLE POINTS 183
2.9 STRUCTURE OF THE SINGULAR SET 188
3 OBSTACLE PROBLEM FOR THE FRACTIONAL LAPLACIAN 201
3.1 CONSTRUCTION OF THE SOLUTION AND BASIC PROPERTIES 202
3.2 LIPSCHITZ CONTINUITY, SEMICONVEXITY AND C ] , A E S T I M A T E S
203 3.3 THIN OBSTACLE FOR THE OPERATOR L A : LOCAL C L ' A E S T I M A T
E S 204
3.4 MINIMIZERS OF THE WEIGHTED RAYLEIGH QUOTIENT AND A MONOTONICITY
FORMULA 206
3.5 OPTIMAL REGULARITY FOR TANGENTIALLY CONVEX GLOBAL SOLUTIONS 207
3.6 FREQUENCY FORMULA 211
3.7 BLOW-UP SEQUENCES AND OPTIMAL REGULARITY 217
3.8 NONDEGENERATE CASE: LIPSCHITZ CONTINUITY OF THE FREE BOUNDARY 225
3.9 BOUNDARY HARNACK PRINCIPLES AND C L A REGULARITY OF THE FREE
BOUNDARY 227
APPENDIX A: THE FRACTIONAL LAPLACIAN 231
DEFINITION AND BASIC PROPERTIES 231
SUPERSOLUTIONS AND COMPARISON 232
APPENDIX B: THE OPERATOR L A 234
DEFINITION AND PRELIMINARY FACTS 234
HARNACK INEQUALITY, LIOUVILLE THEOREM AND MEAN VALUE PROPERTY 236
POINCARE INEQUALITIES 240
APPENDIX C: RELATION BETWEEN {-A) S A N D L A 240
REFERENCES 243
LIST O F PARTICIPANTS 245 |
| any_adam_object | 1 |
| author2 | Gianazza, Ugo |
| author2_role | edt |
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| author_GND | (DE-588)138867941 (DE-588)1018067728 |
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| building | Verbundindex |
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| 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 | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV039995697 |
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| indexdate | 2024-07-21T00:29:27Z |
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| physical | XI, 247 S. graph. Darst. 24 cm |
| publishDate | 2012 |
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| spelling | Regularity estimates for nonlinear elliptic and parabolic problems Cetraro, Italy 2009 Fondazione CIME. John Lewis ... Ed.: Ugo Gianazza ; John Lewis Berlin [u.a.] Springer 2012 XI, 247 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2045 Literaturangaben Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Regularität (DE-588)4049074-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2009 Cetraro gnd-content Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Regularität (DE-588)4049074-9 s DE-604 Lewis, John 1963- Sonstige (DE-588)138867941 oth Gianazza, Ugo (DE-588)1018067728 edt Centro Internazionale Matematico Estivo Sonstige (DE-588)1025933-8 oth Erscheint auch als Online-Ausgabe Regularity Estimates for Nonlinear Elliptic and Parabolic Problems Lecture notes in mathematics 2045 (DE-604)BV000676446 2045 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3911650&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024852740&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Regularity estimates for nonlinear elliptic and parabolic problems Cetraro, Italy 2009 Lecture notes in mathematics Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Regularität (DE-588)4049074-9 gnd |
| subject_GND | (DE-588)4128900-6 (DE-588)4049074-9 (DE-588)1071861417 |
| title | Regularity estimates for nonlinear elliptic and parabolic problems Cetraro, Italy 2009 |
| title_auth | Regularity estimates for nonlinear elliptic and parabolic problems Cetraro, Italy 2009 |
| title_exact_search | Regularity estimates for nonlinear elliptic and parabolic problems Cetraro, Italy 2009 |
| title_full | Regularity estimates for nonlinear elliptic and parabolic problems Cetraro, Italy 2009 Fondazione CIME. John Lewis ... Ed.: Ugo Gianazza ; John Lewis |
| title_fullStr | Regularity estimates for nonlinear elliptic and parabolic problems Cetraro, Italy 2009 Fondazione CIME. John Lewis ... Ed.: Ugo Gianazza ; John Lewis |
| title_full_unstemmed | Regularity estimates for nonlinear elliptic and parabolic problems Cetraro, Italy 2009 Fondazione CIME. John Lewis ... Ed.: Ugo Gianazza ; John Lewis |
| title_short | Regularity estimates for nonlinear elliptic and parabolic problems |
| title_sort | regularity estimates for nonlinear elliptic and parabolic problems cetraro italy 2009 |
| title_sub | Cetraro, Italy 2009 |
| topic | Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Regularität (DE-588)4049074-9 gnd |
| topic_facet | Nichtlineare partielle Differentialgleichung Regularität Konferenzschrift 2009 Cetraro |
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