Interfaces and Free Boundaries

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Volume 7, Issue 1, 2005, pp. 55–78
DOI: 10.4171/IFB/113

Published online: 2005-03-31

Geometric properties of Bernoulli-type minimizers

Arshak Petrosyan[1] and Enrico Valdinoci[2]

(1) Purdue University, West Lafayette, USA
(2) Università di Roma Tor Vergata, 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

Petrosyan Arshak, Valdinoci Enrico: Geometric properties of Bernoulli-type minimizers. Interfaces Free Bound. 7 (2005), 55-78. doi: 10.4171/IFB/113