Moduli of continuity for viscosity solutions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 09 Sep 2015Embargo end date: 01 Nov 2015 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 144, pages 1,717-1,724 (issn: 0002-9939, eissn: 1088-6826,

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Authors: Li, Xiaolong;

doi: 10.1090/proc/12850 , 10.48550/arxiv.1511.02184

arXiv: 1511.02184

Moduli of continuity for viscosity solutions

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Abstract

In this paper, we investigate the moduli of continuity for viscosity solutions of a wide class of nonsingular quasilinear evolution equations and also for the level set mean curvature flow, which is an example of singular degenerate equations. We prove that the modulus of continuity is a viscosity subsolution of some one dimensional equation. This work extends B. Andrews' recent result on moduli of continuity for smooth spatially periodic solutions.

8 pages

Related Organizations

University of California, San Diego
United States

Keywords

viscosity solution, Mathematics - Differential Geometry, Viscosity solutions to PDEs, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), level set mean curvature flow, modulus of continuity, FOS: Mathematics, Geometric evolution equations (mean curvature flow, Ricci flow, etc.), Analysis of PDEs (math.AP)

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