Nonsymmetric elliptic operators with wentzell boundary conditions in general domains


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 Lp-type, 1 ≤ p ≤ ∞. We prove the existence of analytic quasicontractive (C0)-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∞.

Publication Title

Communications on Pure and Applied Analysis