Title: Connections between geometry and PDE in sets with poor connectivity.

Abstract:

How irregular can the boundary of a domain be if we still want nice PDE properties to hold? To answer this (apparently geometric/PDE) question, many authors have shown in the last 50 years that Harmonic Analysis plays a crucial role if we want to consider the most irregular domains as possible.

In this talk, we will show some of the interactions that take place between these 3 disciplines to study domains which lack connectivity in an essential way, and some possible extensions of these results to parabolic PDE.