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A FINER SINGULAR LIMIT OF A SINGLE-WELL MODICA-MORTOLA FUNCTIONAL AND ITS APPLICATIONS TO THE KOBAYASHI-WARREN-CARTER ENERGY
| Title: | A FINER SINGULAR LIMIT OF A SINGLE-WELL MODICA-MORTOLA FUNCTIONAL AND ITS APPLICATIONS TO THE KOBAYASHI-WARREN-CARTER ENERGY |
| Authors: | GIGA, YOSHIKAZU Browse this author | | OKAMOTO, JUN Browse this author | | UESAKA, MASAAKI Browse this author |
| Keywords: | Gamma convergence | | Modica–Mortola functional | | Kobayashi-Warren-Carter energy |
| Issue Date: | 25-Mar-2020 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1130 |
| Start Page: | 1 |
| End Page: | 26 |
| Abstract: | An explicit representation of the Gamma limit of a single-well Modica-Mortola functional is given for one-dimensional space under the graph convergence which is finer than conventional L1-convergence or convergence in measure. As an application, an explicit representation of a singular limit of the Kobayashi-Warren-Carter energy, which is popular in materials science, is given. Some compactness under the graph convergence is also established. Such formulas as well as compactness is useful to characterize the limit of minimizers the Kobayashi-Warren-Carter energy. To characterize the Gamma limit under the graph convergence, a new idea which is especially useful for one-dimensional problem is introduced. It is a change of parameter of the variable by arc-length parameter of its graph, which is called unfolding by the arc-length parameter in this paper. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/77045 |
| 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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