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Journal Articles Nonlinear Analysis: Theory, Methods and Applications Year : 2007

A free boundary problem for the Laplacian with constant Bernoulli-type boundary condition

Abstract

We study a free boundary problem for the Laplace operator, where we impose a Bernoulli-type boundary condition. We show that there exists a solution to this problem. We use A. Beurling's technique, by defining two classes of sub- and supersolutions and a Perron argument. We try to generalize here a previous work of A. Henrot and H. Shahgholian. We extend these results in different directions.
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Dates and versions

hal-00128760 , version 1 (02-02-2007)

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Erik Lindgren, Yannick Privat. A free boundary problem for the Laplacian with constant Bernoulli-type boundary condition. Nonlinear Analysis: Theory, Methods and Applications, 2007, 67 (8), pp.2497-2505. ⟨10.1016/j.na.2006.08.045⟩. ⟨hal-00128760⟩
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