An overdetermined problem with non constant boundary condition
classification
🧮 math.AP
keywords
problemboundaryoverdeterminedsolutionconditionconstantconstraintequation
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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.
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