Semi-bounded Differential Operators, Contractive Semigroups and Beyond

2014
ISBN: 978-3-319-04557-3
Verlag: Springer International Publishing

Buch, Englisch, Band 243, 252 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 5266 g

Reihe: Operator Theory: Advances and Applications

In the present book the conditions are studied for the semi-boundedness of partial differential operators which is interpreted in different ways. Nowadays one knows rather much about L-semibounded differential and pseudo-differential operators, although their complete characterization in analytic terms causes difficulties even for rather simple operators. Until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. The goal of the present book is to partially fill this gap. Various types of semi-boundedness are considered and some relevant conditions which are either necessary and sufficient or best possible in a certain sense are given. Most of the results reported in this book are due to the authors.

Zielgruppe

Research

Autoren/Hrsg.

Maz'ya, Vladimir

Cialdea, Alberto

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

Introduction.- 1 Preliminary facts on semi-boundedness of forms and operators.- 2 Lp-dissipativity of scalar second order operators with complex coefficients.- 3 Elasticity system.- 4 Lp-dissipativity for systems of partial differential operators.- 5 The angle of Lp-dissipativity.- 6 Higher order differential operators in Lp.- 7 Weighted positivity and other related results.- References.