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...
Gespeichert in:
| Hauptverfasser: | , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
08 Jun 2010
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| In: |
Numerical functional analysis and optimization
Year: 2010, Jahrgang: 31, Heft: 4, Pages: 489-517 |
| ISSN: | 1532-2467 |
| DOI: | 10.1080/01630563.2010.485853 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1080/01630563.2010.485853
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| Verfasserangaben: | Peter Elbau, Markus Grasmair, Frank Lenzen & Otmar Scherzer |
MARC
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| 520 | |a 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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| 650 | 4 | |a Geometric partial differential equations | |
| 650 | 4 | |a Mean curvature motion | |
| 650 | 4 | |a Non-convex bound variation | |
| 650 | 4 | |a Non-convex functionals | |
| 650 | 4 | |a Non-convex semi-group theory | |
| 650 | 4 | |a Relaxation | |
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