Nonlocal geometric expansion of convex planar curves

Ben Andrews; Mikhail Feldman

doi:10.1006/jdeq.2001.4107

Nonlocal geometric expansion of convex planar curves

Ben Andrews^*
, Mikhail Feldman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We consider a class of nonlocal geometric equations for expanding curves in the plane, arising in the study of evolutions governed by Monge-Kantorovich mass transfer. We construct convex solutions, given convex initial data. In order to obtain such solutions, we develop a new version of Perron's method. We give applications to the problem of characterizing fast/slow diffusion limits.

Original language	English
Pages (from-to)	298-343
Number of pages	46
Journal	Journal of Differential Equations
Volume	182
Issue number	2
DOIs	https://doi.org/10.1006/jdeq.2001.4107
Publication status	Published - 1 Jul 2002

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10.1006/jdeq.2001.4107

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abstract = "We consider a class of nonlocal geometric equations for expanding curves in the plane, arising in the study of evolutions governed by Monge-Kantorovich mass transfer. We construct convex solutions, given convex initial data. In order to obtain such solutions, we develop a new version of Perron's method. We give applications to the problem of characterizing fast/slow diffusion limits.",

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AB - We consider a class of nonlocal geometric equations for expanding curves in the plane, arising in the study of evolutions governed by Monge-Kantorovich mass transfer. We construct convex solutions, given convex initial data. In order to obtain such solutions, we develop a new version of Perron's method. We give applications to the problem of characterizing fast/slow diffusion limits.

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Nonlocal geometric expansion of convex planar curves

Abstract

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