Speaker: José María Martell Berrocal (ICMAT, Madrid, Spain)
Date: 15 February 2024
Time: 2 pm
Venue: Microsoft Teams (online)
Solvability of the Dirichlet problem with data in $L^p$ for some finite $p$ for elliptic operators, such as the Laplacian,
amounts to showing that the associated elliptic/harmonic measure satisfies a Reverse Hölder inequality. Under strong connectivity
assumptions, it has been proved that such a solvability is equivalent to the fact that that all bounded null-solutions of the
operator in question satisfy Carleson measure estimates. In this talk, we will give a historical overview of this theory and
present some recent results in collaboration with M. Cao and P. Hidalgo where, without any connectivity, we characterize
certain weak Carleson measure estimates for bounded null-solutions in terms of a Corona decomposition for the elliptic measure.
This extends the previous theory to non-connected settings where, as a consequence of our method, we establish
Fefferman-Kenig-Pipher perturbation results.