|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
VISCOSITY SOLUTIONS FOR THE CRYSTALLINE MEAN CURVATURE FLOW WITH A NONUNIFORM DRIVING FORCE TERM
| Title: | VISCOSITY SOLUTIONS FOR THE CRYSTALLINE MEAN CURVATURE FLOW WITH A NONUNIFORM DRIVING FORCE TERM |
| Authors: | GIGA, YOSHIKAZU Browse this author | | POŽÁR, NORBERT Browse this author |
| Issue Date: | 17-Jun-2020 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1132 |
| Start Page: | 1 |
| End Page: | 23 |
| Abstract: | A general purely crystalline mean curvature flow equation with a nonuniform driving force term is considered. The unique existence of a level set flow is established when the driving force term is continuous and spatially Lipschitz uniformly in time. By introducing a suitable notion of a solution a comparison principle of continuous solutions is established for equations including the level set equations. An existence of a solution is obtained by stability and approximation by smoother problems. A necessary equi-continuity of approximate solutions is established. It should be noted that the value of crystalline curvature may depend not only on the geometry of evolving surfaces
but also on the driving force if it is spatially inhomogeneous. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/78580 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
|
Submitter: 数学紀要登録作業用
|
