{"paper":{"title":"A discrete stochastic interpretation of the Dominative $p$-Laplacian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juan J. Manfredi, Karl K. Brustad, Peter Lindqvist","submitted_at":"2018-09-03T20:34:25Z","abstract_excerpt":"The Dominative $p$-Laplacian is the operator defined for $2\\le p < \\infty$ as follows: \\begin{equation}\\label{dominativep} \\mathcal{L}_{p}u(x)=\\frac{1}{p}\\left(\\lambda_{1}+\\ldots+\\lambda_{N-1}\\right)+\\frac{(p-1)}{p}\\lambda_{N},\n  \\end{equation} where we have ordered the eigenvalues of $D^{2}u(x)$ as $\\lambda_{1}\\le \\lambda_{2}\\ldots\\le\\lambda_{N}$. The operator $\\mathcal{L}_{p}u(x)$ was introduced by Brustand to give a natural explanation of the superposition principle for the $p$-Laplace equation.\n  In this paper, we present a discrete stochastic approximation to the unique viscosity solution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00714","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}