Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2022-11-24 DOI:10.1515/cmam-2022-0038

M. Dambrine, H. Harbrecht, B. Puig

引用次数: 0

Abstract

Abstract The present article is concerned with solving Bernoulli’s exterior free boundary problem in the case of an interior boundary that is random. We provide a new regularity result on the map that sends a parametrization of the inner boundary to a parametrization of the outer boundary. Moreover, assuming that the interior boundary is convex, also the exterior boundary is convex, which enables to identify the boundaries with support functions and to determine their expectations. We in particular construct a confidence region for the outer boundary based on Aumann’s expectation and provide a numerical method to compute it.

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不确定条件下的Bernoulli自由边界问题：凸情形

摘要本文研究了随机内边界情况下的伯努利外自由边界问题的求解。我们在映射上提供了一个新的正则性结果，将内边界的参数化发送到外边界的参数化。此外，假设内部边界是凸的，那么外部边界也是凸的，从而可以识别具有支持函数的边界，并确定其期望。特别地，我们基于Aumann期望构造了外边界的置信区域，并给出了计算置信区域的数值方法。

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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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.