{"paper":{"title":"Modica type gradient estimates for an inhomogeneous variant of the normalized p-laplacian evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnid Banerjee, Nicola Garofalo","submitted_at":"2014-11-12T11:49:51Z","abstract_excerpt":"In this paper, we study an inhomogeneous variant of the normalized $p$-Laplacian evolution which has been recently treated in \\cite{BG1}, \\cite{Do}, \\cite{MPR} and \\cite{Ju}. We show that if the initial datum satisfies the pointwise gradient estimate \\eqref{e:main1} a.e., then the unique solution to the Cauchy problem \\eqref{main5} satisfies the same gradient estimate a.e. for all later times, see \\eqref{e:main} below. A general pointwise gradient bound for the entire bounded solutions of the elliptic counterpart of equation \\eqref{main5} was first obtained in \\cite{CGS}. Such estimate general"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3154","kind":"arxiv","version":1},"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"}