The bi-Laplacian with Wentzell boundary conditions on Lipschitz domains

Markus Kunze (Universität Konstanz) #

We present some results about the bi-Laplacian with Wentzell boundary conditions on a bounded domain \(\Omega \subset \mathbb{R}^n\) with Lipschitz boundary \(\Gamma\). Using form methods, we give a rigorous definition of this operator and prove that it generates an analytic and strongly continuous semigroup on the space \(L^2(\Omega)\times L^2(\Gamma)\). We also give a characterization of the domain of this operator in terms of Sobolev spaces and establish Hölder regularity of solutions that will allow us to interpret the boundary conditions in a classical way. Some further properties of solutions are also discussed.

This talk is based on joined work with Robert Denk and David Ploss.