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).
CITATION STYLE
Andrews, B., & Feldman, M. (2002). Nonlocal geometric expansion of convex planar curves. Journal of Differential Equations, 182(2), 298–343. https://doi.org/10.1006/jdeq.2001.4107
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