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


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 Lp spaces (over a fixed measure space), which is analytic in a sector of opening angle Θp, then the maximal choice for Θp is a concave function of 1-1/p. This and related results are applied to give improved estimates on the optimal Lp angle of ellipticity for a parabolic equation of the form ∂u/∂t = Au, where A is a uniformly elliptic second order partial differential operator with Wentzell or dynamic boundary conditions. Similar results are obtained for the higher order equation ∂u/∂t = (-1)m+1Amu, for all positive integers m. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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