Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem

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Abstract

We prove a very general form of the Angle Concavity Theorem, which says that if ((T(t)) defines a one parameter semigroup acting over various L^p spaces (over a fixed measure space), which is analytic in a sector of opening angle heta_p, then the maximal choice for heta_p is aconcave function of 1-1/p. This and related results are applied to get improved estimates on the optimal L^p angle of ellipticity for a parabolic equation of the form {\partial u}{\partial t}=Au, where A is a uniformly elliptic second order partial differential operator with Wentzell or dynamic boundary condition. Similar results are obtained for the higher order equation {\partial u}{\partial t}=(-1)^{m+1}A^m u for all positive integers m.

Autore Pugliese

Tutti gli autori

  • ROMANELLI S.

Titolo volume/Rivista

Non Disponibile

Anno di pubblicazione

2010

ISSN

0025-584X

ISBN

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Numero di citazioni Wos

24

Ultimo Aggiornamento Citazioni

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Numero di citazioni Scopus

26

Ultimo Aggiornamento Citazioni

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Settori ERC

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Codici ASJC

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