自由边界上具有Robin条件的两相问题

Journal de l’École polytechnique — Mathématiques Pub Date : 2020-03-31 DOI:10.5802/jep.139

Serena Guarino Lo Bianco, Domenico Angelo La Manna, B. Velichkov

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引用次数: 2

摘要

首次研究了一类满足Robin边界条件的两相自由边界问题。我们考虑解在自由边界上连续的情况，证明了相关变分问题的极小值的存在性和正则性结果。最后，在附录中，我们给出了一类斯坦纳对称最小化的例子。

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A two-phase problem with Robin conditions on the free boundary

We study for the first time a two-phase free boundary problem in which the solution satisfies a Robin boundary condition. We consider the case in which the solution is continuous across the free boundary and we prove an existence and a regularity result for minimizers of the associated variational problem. Finally, in the appendix, we give an example of a class of Steiner symmetric minimizers.

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Journal de l’École polytechnique — Mathématiques

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