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arXiv · 2209.13448

A pathwise regularization by noise phenomenon for the evolutionary $p$-Laplace equation

Florian Bechtold·Jörn Wichmann
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Abstract

We study an evolutionary $p$-Laplace problem whose potential is subject to a translation in time. Provided the trajectory along which the potential is translated admits a sufficiently regular local time, we establish existence of solutions to the problem for singular potentials for which a priori bounds in classical approaches break down, thereby establishing a pathwise regularization by noise phenomena for this non-linear problem.

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Florian Bechtold, Jörn Wichmann. 2022-09-27. A pathwise regularization by noise phenomenon for the evolutionary $p$-Laplace equation. https://arxiv.org/abs/2209.13448

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