Nonlocal Geometric Expansion of Convex Planar Curves

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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. © 2002 Elsevier Science (USA).

Document Type: Research Article

Affiliations: 1: Centre for Mathematics and Its Applications, Australian National University, ACT 0200, Australia 2: Department of Mathematics, University of Wisconsin, Madison, Wisconsin, 53706

Publication date: July 1, 2002

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