| Abstract: |
| In this talk we present recent results in the direction of solving boundary value
problems for general second-order systems on rough domains with boundary data taken
in non-standard function spaces. More precisely, we study the Dirichlet problem with
boundary data in Herz spaces. We develop a comprehensive Calder\`on-Zygmund theory
for a relevant class of singular integral operators acting on (and from) this brand of
spaces via a powerful extrapolation result, and succeed in employing the method of
boundary layer potentials to establish a well-posedness result for the aforementioned
boundary problem. This is joint work with Marius Mitrea. |
|