Methods and Applications of Analysis

Volume 22 (2015)

Number 2

Bernoulli problem for rough domains

Pages: 131 – 146

DOI: http://dx.doi.org/10.4310/MAA.2015.v22.n2.a1

Authors

François Bouchon (Laboratoire de Mathématiques, Clermont Université, Université Blaise-Pascal, Clermont-Ferrand, France; and CNRS, UMR 6620, LM, Aubière, France)

Laurent Chupin (Laboratoire de Mathématiques, Clermont Université, Université Blaise-Pascal, Clermont-Ferrand, France; and CNRS, UMR 6620, LM, Aubière, France)

Abstract

We consider the exterior free boundary Bernoulli problem in the case of a rough given domain. An asymptotic analysis shows that the solution of the initial problem can be approximated by the solution of a non-rough Bernoulli problem at order $2$. Numerical tests confirm these theoretical results.

Keywords

Bernoulli problem, free boundary, roughness, rugosity

2010 Mathematics Subject Classification

35B27, 35N25, 35R35, 78M35

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Published 1 June 2015