Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem
Angelo Favini, Gisèle Ruiz Goldstein, Jerome A. Goldstein, Enrico Obrecht, Silvia Romanelli · Mathematische Nachrichten · 2010
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 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 +lAmu, for all positive integers m.