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

Authors

Angelo Favini, Alma Mater Studiorum Università di BolognaFollow
Gisèle Ruiz Goldstein, University of MemphisFollow
Jerome A. Goldstein, University of MemphisFollow
Enrico Obrecht, Alma Mater Studiorum Università di Bologna
Silvia Romanelli, Università degli studi di Bari Aldo Moro

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+1Amu, for all positive integers m. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Publication Title

Mathematische Nachrichten

Recommended Citation

Favini, A., Goldstein, G., Goldstein, J., Obrecht, E., & Romanelli, S. (2010). Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem. Mathematische Nachrichten, 283 (4), 504-521. https://doi.org/10.1002/mana.200910086