English

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 pp-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 P\mathbb{P}-a.e. ωΩ\omega \in \Omega and a.e. t(0,)t \in (0,\infty) admits a unique strong solution and to determine asymptotic properties of this solution.

Keywords

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}
}
R2 v1 2026-06-22T22:12:33.652Z