A discrete stochastic interpretation of the dominative p-laplacian

Karl K. Brustad, Peter Lindqvist, Juan J. Manfredi

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We build a discrete stochastic process adapted to the (nonlinear) dominative p-Laplacian Dpu(x):= ∆u + (p − 2)λN, where λN is the largest eigenvalue of D2u and p > 2. We show that the discrete solutions of the Dirichlet problems at scale ε tend to the solution of the Dirichlet problem for Dp as ε → 0. We assume that the domain and the boundary values are both Lipschitz.

Original languageEnglish
Pages (from-to)489-506
Number of pages18
JournalDifferential and Integral Equations
Volume33
Issue number9-10
Publication statusPublished - Sep 2020
MoE publication typeA1 Journal article-refereed

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