Analysis of heat equations on domains:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton Univ. Press
2005
|
| Series: | London Mathematical Society monographs
N.S., 31 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 284 S. |
| ISBN: | 0691120161 |
Staff View
MARC
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| 650 | 4 | |a Spektraltheorie - Elliptischer Differentialoperator - Wärmeleitungsgleichung | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Notation xiii
Chapter 1. SESQUILINEAR FORMS, ASSOCIATED OPERATORS, AND
SEMIGROUPS 1
1.1 Bounded sesquilinear forms 1
1.2 Unbounded sesquilinear forms and their associated operators 3
1.3 Semigroups and unbounded operators 18
1.4 Semigroups associated with sesquilinear forms 29
1.5 Correspondence between forms, operators, and semigroups 38
Chapter 2. CONTRACTIVITY PROPERTIES 43
2.1 Invariance of closed convex sets 44
2.2 Positive and Lp contractive semigroups 49
2.3 Domination of semigroups 58
2.4 Operations on the form domain 64
2.5 Semigroups acting on vector valued functions 68
2.6 Sesquilinear forms with nondense domains 74
Chapter 3. INEQUALITIES FOR SUB MARKOVIAN SEMIGROUPS 79
3.1 Sub Markovian semigroups and Kato type inequalities 79
3.2 Further inequalities and the corresponding domain in Lp 88
3.3 Lp holomorphy of sub Markovian semigroups 95
Chapter 4. UNIFORMLY ELLIPTIC OPERATORS ON DOMAINS 99
4.1 Examples of boundary conditions 99
4.2 Positivity and irreducibility 103
4.3 L°° contractivity 107
4.4 The conservation property 120
4.5 Domination 125
4.6 I/p contractivity for 1 p oo 134
4.7 Operators with unbounded coefficients 137
Chapter 5. DEGENERATE ELLIPTIC OPERATORS 143
5.1 Symmetric degenerate elliptic operators 144
5.2 Operators with terms of order 1 145
Viii CONTENTS
Chapter 6. GAUSSIAN UPPER BOUNDS FOR HEAT KERNELS 155
6.1 Heat kernel bounds, Sobolev, Nash, and
Gagliardo Nirenberg inequalities 155
6.2 Holder continuity estimates of the heat kernel 160
6.3 Gaussian upper bounds 163
6.4 Sharper Gaussian upper bounds 174
6.5 Gaussian bounds for complex time and Lp analyticity 180
6.6 Weighted gradient estimates 185
Chapter 7. GAUSSIAN UPPER BOUNDS AND LP SPECTRAL THEORY 193
7.1 Lp bounds and holomorphy 196
7.2 Lp spectral independence 204
7.3 Riesz means and regularization of the Schrodinger group 208
7.4 Lp estimates for wave equations 214
7.5 Singular integral operators on irregular domains 228
7.6 Spectral multipliers 235
7.7 Riesz transforms associated with uniformly elliptic operators 240
7.8 Gaussian lower bounds 245
Chapter 8. A REVIEW OF THE KATO SQUARE ROOT PROBLEM 253
8.1 The problem in the abstract setting 253
8.2 The Kato square root problem for elliptic operators 257
8.3 Some consequences 261
Bibliography 265
Index 283
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV020038925 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:11:26Z |
| institution | BVB |
| isbn | 0691120161 |
| language | English |
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| physical | XI, 284 S. |
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| spelling | Ouhabaz, El-Maati Verfasser (DE-588)113444265 aut Analysis of heat equations on domains El Maati Ouhabaz Princeton [u.a.] Princeton Univ. Press 2005 XI, 284 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society monographs N.S., 31 Halbgruppe - Partielle Differentialgleichung Spektraltheorie - Elliptischer Differentialoperator - Wärmeleitungsgleichung Heat equation Heat Transmission Measurement Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Wärmeleitungsgleichung (DE-588)4188859-5 gnd rswk-swf Elliptischer Differentialoperator (DE-588)4140057-4 gnd rswk-swf Elliptischer Differentialoperator (DE-588)4140057-4 s Spektraltheorie (DE-588)4116561-5 s Wärmeleitungsgleichung (DE-588)4188859-5 s DE-604 London Mathematical Society monographs N.S., 31 (DE-604)BV045355493 31 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013360033&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ouhabaz, El-Maati Analysis of heat equations on domains London Mathematical Society monographs Halbgruppe - Partielle Differentialgleichung Spektraltheorie - Elliptischer Differentialoperator - Wärmeleitungsgleichung Heat equation Heat Transmission Measurement Spektraltheorie (DE-588)4116561-5 gnd Wärmeleitungsgleichung (DE-588)4188859-5 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4188859-5 (DE-588)4140057-4 |
| title | Analysis of heat equations on domains |
| title_auth | Analysis of heat equations on domains |
| title_exact_search | Analysis of heat equations on domains |
| title_full | Analysis of heat equations on domains El Maati Ouhabaz |
| title_fullStr | Analysis of heat equations on domains El Maati Ouhabaz |
| title_full_unstemmed | Analysis of heat equations on domains El Maati Ouhabaz |
| title_short | Analysis of heat equations on domains |
| title_sort | analysis of heat equations on domains |
| topic | Halbgruppe - Partielle Differentialgleichung Spektraltheorie - Elliptischer Differentialoperator - Wärmeleitungsgleichung Heat equation Heat Transmission Measurement Spektraltheorie (DE-588)4116561-5 gnd Wärmeleitungsgleichung (DE-588)4188859-5 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd |
| topic_facet | Halbgruppe - Partielle Differentialgleichung Spektraltheorie - Elliptischer Differentialoperator - Wärmeleitungsgleichung Heat equation Heat Transmission Measurement Spektraltheorie Wärmeleitungsgleichung Elliptischer Differentialoperator |
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