Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case

Author:

Dambrine Marc1,Harbrecht Helmut2ORCID,Puig Benedicte1

Affiliation:

1. Laboratoire de Mathématiques et de leurs Applications de Pau – UMR CNRS 5142 , Université de Pau et des Pays de l’Adour , Pau , France

2. Department of Mathematics and Computer Science , University of Basel , Basel , Switzerland

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Recent Advances in Boundary Element Methods;Computational Methods in Applied Mathematics;2023-03-28

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