An overdetermined problem with non constant boundary condition

Abstract

We investigate an overdetermined Torsion problem, with a non-constant positively homogeneous boundary constraint on the gradient. We interpret this problem as the Euler equation of a shape optimization problems, we prove existence and regularity of a solution. Moreover several geometric properties of the solution are shown.

Cited by in corpus (3)

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• On a two-phase Serrin-type problem and its numerical computation
• A shape optimization problem in cylinders and related overdetermined problems