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 \theta_p, then the maximal choice for \theta_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.
Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem
ROMANELLI, Silvia
2010-01-01
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 \theta_p, then the maximal choice for \theta_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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
