Bernoulli free boundary problems under uncertainty: the convex case

Dambrine, Marc and Harbrecht, Helmut and Puig, Benedicte. (2023) Bernoulli free boundary problems under uncertainty: the convex case. Computational Methods in Applied Mathematics, 23 (2). pp. 333-352.

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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 iden- tify 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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:De Gruyter
Note:Publication type according to Uni Basel Research Database: Journal article
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edoc DOI:
Last Modified:08 May 2023 10:22
Deposited On:17 Apr 2023 08:43

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