A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition |
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| Authors: | Erik Lindgren Yannick Privat |
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| Affiliation: | 1. Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden;2. Institut Élie Cartan de Nancy, Université Henri Poincaré Nancy 1, B.P. 239, Vandœuvre-lés-Nancy Cedex, France |
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| 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 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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