Variational Evolution Problems and Nonlocal Geometric Motion |
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Authors: | Mikhail Feldman |
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Institution: | (1) Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730, US |
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Abstract: | We consider two variational evolution problems related to Monge-Kantorovich mass transfer. These problems provide models
for collapsing sandpiles and for compression molding. We prove the following connection between these problems and nonlocal
geometric curvature motion: The distance functions to surfaces moving according to certain nonlocal geometric laws are solutions
of the variational evolution problems. Thus we do the first step of the proof of heuristics developed in earlier works. The
main techniques we use are differential‐equation methods in the Monge‐Kantorovich theory.
(Accepted May 19, 1998) |
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