| 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. |
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