"Sharp Boundary Trace Theory and Schrodinger Operators on Bounded Lipschitz Domains''
Abstract: We develop a sharp boundary trace theory in arbitrary bounded
Lipschitz domains which, in contrast to classical results, allows forbidden endpoints in the Sobolev scale and permits the consideration of functions exhibiting very limited regularity. This is done at the (necessary) expense of stipulating an additional regularity condition involving the action of the Laplacian. This boundary trace theory serves as a platform for developing a spectral theory for Schrodinger operators on bounded Lipschitz domains, along with their associated Weyl-Titchmarsh operators. The talk is based on joint work with Fritz Gesztesy and Marius Mitrea.