Interfaces and Free Boundaries

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Volume 7, Issue 1, 2005, pp. 55–78

DOI: 10.4171/IFB/113

Geometric properties of Bernoulli-type minimizers

Arshak Petrosyan (1) and Enrico Valdinoci (2)

(1) Department of Mathematics, University of Texas at Austin, TX 78712, AUSTIN, UNITED STATES
(2) Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00133, ROMA, ITALY

We consider a Bernoulli-type variational problem and we prove some geometric properties for minimizers, such as: gradient bounds, linear growth from the free boundary, density estimates, uniform convergence of level sets and the existence of plane-like minimizers in periodic media.

Keywords: free boundary problem, Bernoulli-type problem, $p$-Laplacian, density estimates, plane-like minimizers