Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case-Reference-Cited by-同舟云学术

Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case

Published:2022-11-24 Issue:2 Volume:23 Page:333-352
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Dambrine Marc¹,Harbrecht Helmut²^ORCID,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

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2022-0038/pdf

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