通过电位法解决穆林斯-塞克尔卡问题

Pub Date : 2024-02-23 DOI:10.1002/mana.202300350

Joachim Escher, Anca-Voichita Matioc, Bogdan-Vasile Matioc

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引用次数: 0

摘要

研究表明，二维 Mullins-Sekerka 问题在所有具有 .这是第一个在无界几何中建立这一问题的结果。我们方法的新颖之处在于利用势理论将模型表述为一个由奇异积分算子表示的非线性演化问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Mullins–Sekerka problem via the method of potentials

It is shown that the two-dimensional Mullins–Sekerka problem is well-posed in all subcritical Sobolev spaces $H^{r} (R)$ with $r \in (3 / 2, 2)$ . This is the first result, where this issue is established in an unbounded geometry. The novelty of our approach is the use of the potential theory to formulate the model as an evolution problem with nonlinearities expressed by singular integral operators.

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