Boundary Regularity for Elliptic Partial Differential Equations

11.02.2020, 16:30-17:00  –  Haus 9, Raum 2.22

Philipp Bartmann

The behaviour of solutions to elliptic PDE's at the boundary of a domain $\Omega$ depends heavily on the geometry of $\partial\Omega$. One is therefore interested in criteria to $\Omega$ that ensure differentiability, Hölder-continuity or even more regularity up to the boundary.
We will give a brief overview on the classical results in this regard and introduce an optimal geometric condition - so called $\gamma$-convexity - that guarantees differentiability at the boundary.