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

Abstract

AbstractWe 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 nonlinear problem.