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Isoperimetric inequality for an interior free boundary problem with \(p\)-Laplacian operator. (English) Zbl 1070.35137

Summary: By considering the \(p\)-Laplacian operator, we establish an existence and regularity result for a shape optimization problem. From a monotony result, we show the existence of a solution to the interior problem with a free surface for a family of Bernoulli constants. We also give an optimal estimation for the upper bound of the Bernoulli constant.

MSC:

35R35 Free boundary problems for PDEs
35J70 Degenerate elliptic equations
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