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Progress in the Problem of the Lp-Contractivity of Semigroups for Partial Differential Operators

  • Alberto Cialdea
Chapter
Part of the International Mathematical Series book series (IMAT, volume 13)

Abstract

This is a survey of results concerning the L p -dissipativity of partial differential operators and the L p -contractivity of the generated semigroups, mostly obtained by V. Maz’ya, G. Kresin, M. Langer, and A. Cialdea. Necessary and sufficient conditions are discussed for scalar second order operators with complex coefficients and some systems, including the two-dimensional elasticity. The case of higher order operators is reviewed as well.

Keywords

Cauchy Problem Dirichlet Problem Heat Kernel Elliptic Operator Erential Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità della BasilicataViale dell’AteneoItaly

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