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Moduli of continuity for viscosity solutions


Author: Xiaolong Li
Journal: Proc. Amer. Math. Soc. 144 (2016), 1717-1724
MSC (2010): Primary 53C44; Secondary 35D40
Published electronically: September 9, 2015
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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.


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Xiaolong Li
Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093
Email: xil117@ucsd.edu

DOI: https://doi.org/10.1090/proc/12850
Keywords: Modulus of continuity, viscosity solution, level set mean curvature flow
Received by editor(s): April 17, 2015
Published electronically: September 9, 2015
Communicated by: Michael Wolf
Article copyright: © Copyright 2015 American Mathematical Society