向量值、高阶及非极小化Bernoulli问题的最优正则性
Optimal regularity for vectorial, higher order and non-minimizing Bernoulli problems
- Universität Leipzig, Mathematisches Institut（莱比锡大学数学研究所）
- Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK（格勒诺布尔阿尔卑斯大学）
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中文总结 AI 辅助
本文提出不依赖粘性解或比较方法的新技术，证明向量值、高阶及非极小化Bernoulli自由边界问题解的Lipschitz最优正则性，并推广至弹性、双调和及Stokes方程及二维标准问题。
中文摘要 AI 辅助
我们证明了一大类广义Bernoulli自由边界问题在向量值、高阶及非极小化情形下解的Lipschitz正则性。我们的方法不依赖于粘性解概念或比较方法，这使得我们能够达到与不满足任何极大值原理的椭圆算子（即弹性方程、双调和方程和Stokes方程）相关的Bernoulli型问题的最优正则性。采用类似方法，我们获得了二维标准Bernoulli问题驻定、非极小化解的最优Lipschitz正则性。
英文摘要
We prove the Lipschitz regularity of solutions for a wide class of generalized Bernoulli free boundary problems, in vectorial, higher order, and non-minimizing settings. Our method does not rely on notions of viscosity solutions or comparison methods, which allows us to reach the optimal regularity for Bernoulli-type problems associated to elliptic operators which do not satisfy any maximum principle, namely the elasticity, biharmonic and Stokes equation. With a similar method we obtain the optimal Lipschitz regularity for stationary, non-minimizing solutions of the standard Bernoulli problem in two dimensions.
