单侧两相伯努利自由边界问题

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-01-15 DOI:10.1016/j.matpur.2025.103659

Lorenzo Ferreri , Bozhidar Velichkov

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引用次数: 0

摘要

研究了一类两相满足不可穿透条件的自由边界问题。确切地说，我们有两个在其支点上是谐波的有序正函数，它们在自由边界的单相部分满足伯努利条件，在自由边界的崩塌部分满足传输条件。对于这类双膜型问题，我们证明了具有连续锐模的ε -正则定理。准确地说，我们证明了在平坦点处，两个边界中的每一个都是C1,12正则曲面，并且剩下的奇异集具有最多N−5的Hausdorff维数，其中N是空间的维数。

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A one-sided two phase Bernoulli free boundary problem

We study a two-phase free boundary problem in which the two-phases satisfy an impenetrability condition. Precisely, we have two ordered positive functions, which are harmonic in their supports, satisfy a Bernoulli condition on the one-phase part of the free boundary and a transmission condition on the collapsed part of the free boundary. For this two-membrane type problem, we prove an epsilon-regularity theorem with sharp modulus of continuity. Precisely, we show that at flat points each of the two boundaries is

C^{1, \frac{1}{2}}

regular surface and that the remaining singular set has Hausdorff dimension at most

N - 5

, where N is the dimension of the space.

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来源期刊

Journal de Mathematiques Pures et Appliquees 数学-数学

CiteScore

4.30

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Published from 1836 by the leading French mathematicians, the Journal des Mathématiques Pures et Appliquées is the second oldest international mathematical journal in the world. It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.