Evolution by Non-Convex Functionals |
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Authors: | Peter Elbau Markus Grasmair Frank Lenzen |
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Affiliation: | 1. Johann Radon Institute for Computational and Applied Mathematics (RICAM) , Linz, Austria;2. Computational Science Center , University of Vienna , Austria;3. Heidelberg Collaboratory for Image Processing (HCI) , University of Heidelberg , Germany |
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Abstract: | We establish a semi-group solution concept for flows that are generated by generalized minimizers of non-convex energy functionals. We use relaxation and convexification to define these generalized minimizers. The main part of this work consists in exemplary validation of the solution concept for a non-convex energy functional. For rotationally invariant initial data it is compared with the solution of the mean curvature flow equation. The basic example relates the mean curvature flow equation with a sequence of iterative minimizers of a family of non-convex energy functionals. Together with the numerical evidence this corroborates the claim that the non-convex semi-group solution concept defines, in general, a solution of the mean curvature equation. |
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Keywords: | Geometric partial differential equations Mean curvature motion Non-convex bound variation Non-convex functionals Non-convex semi-group theory Relaxation |
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