Oberseminar AG Analysis - Dr. Simone Ciani, University of Bologna, Italy

Wiener's Criterion for Degenerate Double-Phase Parabolic Equations

We will introduce the Wiener Criterion for the continuity at the boundary for solutions to quasilinear degenerate parabolic equations, with measurable and bounded coefficients.
Then we will specialize to degenerate double-phase equations, showing a sufficiency criterion through the trade-off between the local behaviour of the phase, and the p,q - capacity of the boundary around the point. 
This last part is based on a recent work with Eurica Henriques and Igor Skrypnik.