Isoperimetric inequality for an interior free boundary problem with p-laplacian operator

Abstract

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.

Keywords

• Bernoulli free boundary problem
• starshaped domain
• shape optimization
• shape derivative
• monotony.