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

Erik Lindgren (1) , Yannick Privat (2, 3)

1 Department of Mathematics Royal Institute of technology
2 IECN - Institut Élie Cartan de Nancy
3 CORIDA - Robust control of infinite dimensional systems and applications

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.

Mots clés: free boundary problem; Laplacian; convex analysis; shape optimization

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

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⟩