Analysis and Mathematical Physics

The question of asbolute continuity, with respect to the reference measure, of the harmonic measure on a domain with rough boundary has been the object of many important results. Here we ask about the similar question, but where the Dirichlet condition $u=0$ on the boundary is replaced by the softer Robin condition $\frac{\partial u}{\partial n} + a u = 0$ (where, say $a>0$ is a constant).

We describe the connection with the lung and joint work with S. Decio, M. Engelstein, M. Filoche, S. Mayboroda, M. Michetti.