A randomized weighted $p$-Laplacian evolution equation with Neumann boundary conditions
Functional Analysis
2018-01-15 v3
Abstract
The purpose of this paper is to show that the randomized weighted -Laplacian evolution equation given by \begin{align} \label{eveqrand} \begin{cases} U^{\prime}(t)(\omega) =\text{Div} \left( g(\omega) |DU(t)(\omega)|^{p-2}DU(t)(\omega) \right) \text{ on } S, g(\omega)|DU(t)(\omega)|^{p-2}DU(t)(\omega)\cdot\eta=0 \text{ on } \partial S, U(0)(\omega)=u(\omega),\end{cases} \end{align} for -a.e. and a.e. admits a unique strong solution and to determine asymptotic properties of this solution.
Cite
@article{arxiv.1710.04892,
title = {A randomized weighted $p$-Laplacian evolution equation with Neumann boundary conditions},
author = {Alexander Nerlich},
journal= {arXiv preprint arXiv:1710.04892},
year = {2018}
}