|Apr 03, 2019
|University of Turku
In this presentation we will go over regularity of minimizers under Musielak-Orlicz growth conditions. The main focus will be in the assumptions that generalize for example log-Hölder continuity from the p(x)-case and q/p \leq 1+ \alpha /n from the double phase case. As an example of these assumptions in use, we prove Sobolev-Poincare inequality and sketch a proof for higher integrability of the gradient of a minimizer.