The Regularity Problem for the Laplace Equation in Rough Domains

Explore recent advances in Boundary Value Problems for the Laplace operator with rough boundary data in bounded corkscrew domains. Delve into the equivalence between solvability of the Dirichlet problem for the Laplacian with L^p' boundary data and solvability of the regularity problem with Sobolev space W^1,p boundary data. Examine the geometric assumptions for two-sided chord-arc domains and their implications for Carlos Kenig's 1991 question. Learn about the collaborative work with Xavier Tolsa on this topic, focusing on domains in R^n+1 with uniformly n-rectifiable boundaries and measure theoretic boundaries aligning with topological boundaries.

Mihalis Mourgoglou: The regularity problem for the Laplace equation in rough domains