Oberseminar AG Analysis - Dr. Joachim Rehberg, WIAS Berlin

On non-smooth elliptic and parabolic problems

The talk gives an overview on results concerning elliptic and parabolic regularity, in particular those, received with Prof. Haller during the last 15 years. This affects on hand elliptic isomorphisms like
\[
W^{1,q}_D(\Omega) \ni u \mapsto -\nabla \cdot \mu \nabla u + u \in W^{-1,q}_D(\Omega).
\]
On the other hand, we give an overview on basic facts on maximal parabolic regularity -- often considered as 'folklore' -- but in fact forming the basis for many non-trivial results.