Nonlocal Geometric Expansion of Convex Planar Curves |
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| Authors: | Ben AndrewsMikhail Feldman |
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| Institution: | Centre for Mathematics and Its Applications, Australian National University, ACT 0200, Australiaf1ben.andrews@anu.edu.auf1 Department of Mathematics, University of Wisconsin, Madison, Wisconsin, 53706, f2feldman@math.wisc.eduf2 |
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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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