Joint BCAM-UPV/EHU Analysis and PDE seminar: The regularity problem for the Laplace equation in rough domains

LOCATION: 0.15 room at UPV/EHU and Online

Abstract
In this talk I will present some recent advances on Boundary Value Problems for the Laplace operator with rough boundary data in a bounded corkscrew domain in Rn+1 whose boundary is uniformly n-rectifiable. In particular, I will discuss the equivalence between solvability of the Dirichlet problem for the Laplacian with boundary data in Lp 0 and solvability of the regularity problem for the Laplacian with boundary data in an appropriate Sobolev space W1,p, where p ∈ (1, 2 + ε) and 1/p + 1/p0 = 1. As two-sided chord-arc domains satisfy the aforementioned geometric assumptions, our result answers a question posed by Carlos Kenig in 1991. This is joint work with Xavier Tolsa.

Link to the session: 
https://us06web.zoom.us/j/99649860282?pwd=SE0vemtYMFlwbFBNTXQyOTBONG0vZz09

More info at https://sites.google.com/view/apdebilbao/home