We consider a free boundary problem for the p-Laplace operator
which is related to the so-called Bernoulli free boundary problem.
In this formulation, the classical boundary gradient condition is replaced
by a condition on the distance between two di erent level surfaces of
the solution. For suitable scalings our model converges to the classical
Bernoulli problem; one of the advantages in this new formulation lies in
the simplicity of the arguments, since one does not need to consider the
We shall study this problem in convex and other regimes, and establish
existence and qualitative theory
CitacióGonzález, M.; Gualdani, M.; Shagholian, H. "A discrete bernoulli free boundary problem". 2012.