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

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ISBN-13:
9781400826483
Einband:
Ebook
Seiten:
296
Autor:
El-Maati Ouhabaz
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
2 - DRM Adobe
Sprache:
Englisch
Beschreibung:
Preface ixNotation 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
This is the first comprehensive reference published on heat equations associated with non self-adjoint uniformly elliptic operators. The author provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. He then treats Lp properties of solutions to a wide class of heat equations that have been developed over the last fifteen years. These primarily concern the interplay of heat equations in functional analysis, spectral theory and mathematical physics.

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