Martin Ulmer will give a talk at 10/15/2024.

The Dirichlet problem is the most studied boundary value problem for elliptic PDEs, and has a rich history going back to the beginning of the 20th century. Essentially, the Dirichlet problem asks whether we can find a harmonic function (or a solution to $Lu=0$) that obtains given boundary data $f$. In this talk I will capture the most important results regarding the classical Dirichlet problem, before I will give a detailed introduction to the Dirichlet problem with boundary data in $L^p$. We will get to know the elliptic measure and show a classification of solvability of the Dirichlet problem by Muckenhoupt weights which connects elliptic PDEs with Harmonic Analysis.