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Birkhäuser - Birkhäuser Mathematics | Semi-bounded Differential Operators, Contractive Semigroups and Beyond

Semi-bounded Differential Operators, Contractive Semigroups and Beyond

Cialdea, Alberto, Maz'ya, Vladimir

2014, XIII, 252 p.

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  • ​Treatment of a subject that has hardly been worked in so far
  • No comparable book on the market, no significant intersections with existing monographic literature
  • Most results obtained by the authors themselves

This book examines the conditions for the semi-boundedness of partial differential operators, which are interpreted in different ways. For example, today we know a great deal about L2-semibounded differential and pseudodifferential operators, although their complete characterization in analytic terms still poses difficulties, even for fairly simple operators. In contrast, 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. This book works to address that gap. As such, various types of semi-boundedness are considered and a number of relevant conditions which are either necessary and sufficient or best possible in a certain sense are presented. The majority of the results reported on are the authors’ own contributions.

Content Level » Research

Keywords » L^p-dissipativity - elasticity system - partial differential operators - semi-boundedness - weighted positivity

Related subjects » Birkhäuser Mathematics

Table of contents 

​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.

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