Ouhabaz Analysis of Heat Equations on Domains. (LMS-31)

Course Book
ISBN: 978-1-4008-2648-3
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 31, 296 Seiten

Reihe: London Mathematical Society Monographs

No detailed description available for "Analysis of Heat Equations on Domains. (LMS-31)".

Autoren/Hrsg.

Ouhabaz, El-Maati

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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 L1-contractivity 107
4.4 The conservation property 120
4.5 Domination 125
4.6 Lp-contractivity for 1 p-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 Schrödinger 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

Über Autor(innen)

El-Maati Ouhabaz is Professor of Analysis and Geometry at Université Bordeaux 1