A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition. (English summary) Nonlinear Anal. 67 (2007), no. 8, 2497–2505. Summary: “We study a free boundary problem for the Laplace operator with 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 super-solutions 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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