As part of the MSU Mathematics Lecture Series, Professor Dorina Mitrea, from the University of Missouri, will be presenting : “The Dirichlet Problem for the Laplace-Beltrami Operator in Riemannian Manifolds”. This presentation is scheduled for Tuesday March 19 at 3:00PM in Cheek 175. Everyone is welcome to attend!
Abstract:
We will discuss the Dirichlet problem for the Laplace-Beltrami operator acting on scalar functions in regular Semmes-Kenig-Toro subdomains of a Riemannian manifold M. When all objects and structures involved are smooth the standard elliptic theory based on pseudodifferential operator methods applies. In our work we consider rough subdomains of M, a setting which renders the latter approach ill-suited. As an alternative, we resort to the theory of singular integral operators with variable coefficient kernels on uniformly rectifiable sets which we further refine and adapt to the present framework.