Konferenzraum 614 (Mathegebäude)

The speaker will discuss the solvability of Dirichlet problems for Laplace`s equation when the boundary data is not smooth enough for the existence of a weak solution in usual Sobolev spaces. The generalized harmonic functions will be introduced. Their norms are defined using series expansions involving harmonic Steklov eigenfunctions. We will explain that the usual trace operator has a continuous extension to an isometric isomorphism of specific spaces. This provides a characterization of the generalized solutions of harmonic Dirichlet problems. Numerical simulations of a model problem will be given. This problem is related to the dewetting of thin films. The speaker will discuss the associated phenomenology.

Prof. Petr Kloucek

Universite de Neuchatel