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Article Dans Une Revue Computational Methods in Applied Mathematics Année : 2023

Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case

Helmut Harbrecht
Benedicte Puig
  • Fonction : Auteur

Résumé

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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Dates et versions

hal-04469876 , version 1 (04-04-2024)

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Marc Dambrine, Helmut Harbrecht, Benedicte Puig. Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case. Computational Methods in Applied Mathematics, 2023, 23 (2), pp.333-352. ⟨10.1515/cmam-2022-0038⟩. ⟨hal-04469876⟩
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