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\ud for all positive integers m

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We study nonsymmetric second order elliptic operators with Wentzell boundary conditions in general domains with sufficiently smooth boundary. The ambient space is a space of L p -type, 1 ≤ p ≤ ∞. We prove the existence of analytic quasicontractive (C 0 )-semigroups generated by the closures of such operators, for any 1 < p < ∞. Moreover, we extend a previous result concerning the continuous dependence of these semigroups on the coefficients of the boundary condition. We also specify precisely the domains of the generators explicitly in the case of bounded domains and 1 < p < ∞, when all the ingredients of the problem, including the boundary of the domain, the coefficients, and the initial condition, are of class C ∞ .

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