Special Session 108: Regularity in local versus nonlocal problems

Carleson-type removability for $p$-parabolic equations
Leah Schaetzler
Aalto University
Finland
Co-Author(s):    Micha{\l} Borowski, Theo Elenius, and David Stolnicki
Abstract:
In this talk, I will characterize removable sets for H{\o}lder continuous solutions to degenerate PDEs of parabolic $p$-Laplace type. I will give sufficient and necessary conditions for a set to be removable in terms of an intrinsic parabolic Hausdorff measure, which depends on the considered H{\o}lder exponent. Our method of proof for the sufficient condition only relies on fundamental properties of the obstacle problem and supersolutions and is applicable to a wide class of operators. To obtain the necessary condition, we establish the H{\o}lder continuity of solutions to measure data problems under a certain decay assumption on the considered measure. The talk is based on joint work with Micha{\l} Borowski, Theo Elenius, and David Stolnicki.