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Hokkaido University Preprint Series in Mathematics >
On the motion by singular interfacial energy
| Title: | On the motion by singular interfacial energy |
| Authors: | Giga, Y. Browse this author | | Paolini, M. Browse this author | | Rybka, P. Browse this author |
| Keywords: | singular energies | | geometric subdifferentials | | canonical restrictions | | facets | | curvature flow |
| Issue Date: | 1-Nov-2000 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 498 |
| Start Page: | 1 |
| End Page: | 21 |
| Abstract: | Anisotropic curvature flow equations with singular interfacial energy are important for good unders_tanding of motion of phase-boundaries. If the energy and the interfacial surface were smooth, then the speed of the interface would be equal to the gradient of the energy. However, this is not so simple in the case of non-smooth crystalline energy. But it's well-known that a unique gradient characterization of the velocity is possible if the interface is a curve in the two-dimensional space. In this paper we propose a notion of solution in the three-dimensional space by introducing geometric subdifferentials and characterizing the speed. We also give a counterexample to a problem concerning the Cahn-Hoffman vector field on a facet, a flat portion of the interface. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69248 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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