Evolution by non-convex functionals
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...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
08 Jun 2010
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| In: |
Numerical functional analysis and optimization
Year: 2010, Volume: 31, Issue: 4, Pages: 489-517 |
| ISSN: | 1532-2467 |
| DOI: | 10.1080/01630563.2010.485853 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1080/01630563.2010.485853
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| Author Notes: | Peter Elbau, Markus Grasmair, Frank Lenzen & Otmar Scherzer |
| Summary: | 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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| Item Description: | Gesehen am 06.03.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1532-2467 |
| DOI: | 10.1080/01630563.2010.485853 |