José María Martell - Layer Potentials, Extrapolation and Boundary Value Problems in Unbounded Domains

Explore boundary value problems for elliptic systems with constant complex coefficients in unbounded domains through this 48-minute lecture by José María Martell at the Hausdorff Center for Mathematics. Delve into recent joint research that employs the method of layer potentials to construct unique solutions for domains with unit normals of small oscillation. Learn how the invertibility of a natural operator is demonstrated using a Neumann series. Discover how this approach allows for the consideration of boundary value problems with data in Lebesgue spaces with Muckenhoupt weights. Examine how a sharpened version of the Rubio extrapolation theorem leads to well-posedness of boundary value problems in weighted Banach function spaces.