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Archive for Rational Mechanics and Analysis

, Volume 211, Issue 2, pp 419–453 | Cite as

A Comparison Principle for Singular Diffusion Equations with Spatially Inhomogeneous Driving Force for Graphs

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Abstract

We introduce the notions of viscosity super- and subsolutions suitable for singular diffusion equations of non-divergence type with a general spatially inhomogeneous driving term. In particular, the viscosity super- and subsolutions support facets and allow a possible facet bending. We prove a comparison principle by a modified doubling variables technique. Finally, we present examples of viscosity solutions. Our results apply to a general crystalline curvature flow with a spatially inhomogeneous driving term for a graph-like curve.

Keywords

Viscosity Solution Comparison Principle Obstacle Problem Variational Solution Admissible Function 
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© The Author(s) 2013

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan
  2. 2.Institute of Applied Mathematics and MechanicsWarsaw UniversityWarsawPoland

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