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arXiv · 2205.14314

On a singular limit of the Kobayashi--Warren--Carter energy

Yoshikazu Giga·Jun Okamoto·Koya Sakakibara·Masaaki Uesaka
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Abstract

By introducing a new topology, a representation formula of the Gamma limit of the Kobayashi-Warren-Carter energy is given in a multi-dimensional domain. A key step is to study the Gamma limit of a single-well Modica-Mortola functional. The convergence introduced here is called the sliced graph convergence, which is finer than conventional $L^1$ convergence, and the problem is reduced to a one-dimensional setting by a slicing argument.

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Yoshikazu Giga, Jun Okamoto, Koya Sakakibara, Masaaki Uesaka. 2022-05-28. On a singular limit of the Kobayashi--Warren--Carter energy. https://arxiv.org/abs/2205.14314

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