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

Wichmann J, Bechtold F. A pathwise regularization by noise phenomenon for the evolutionary $p$-Laplace equation. arXiv:2209.13448. 2022.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