Alejandro J. Castro: Layer potentials methods for Dirichlet and Neumann parabolic problems of divergence type with rough coefficients

Abstract: The goal of this talk is to establish solvability of Dirichlet, Neumann and regularity problems for divergence-form heat equations with non-smooth diffusion coefficients.

This is achieved in two main steps: boundedness and invertibility of the relevant layer-potentials. We will consider in detail the case of Hölder coefficients and briefly the situation with merely bounded coefficients.