Bernoulli free boundary problems under uncertainty: the convex case

Dambrine, M. and Harbrecht, H. and Puig, B.. (2022) Bernoulli free boundary problems under uncertainty: the convex case. Preprints Fachbereich Mathematik, 2022 (04).


Official URL: https://edoc.unibas.ch/87829/

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The present article is concerned with solving Bernoulli's exterior free boundary problem in case of an interior boundary which 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, by 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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut
Item Type:Preprint
Publisher:Universität Basel
edoc DOI:
Last Modified:11 Feb 2022 14:27
Deposited On:11 Feb 2022 14:27

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