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 problem, we prove existence and regularity of a solution. Moreover several geometric properties of the solution are shown.
An overdetermined problem with non-constant boundary condition / Chiara Bianchini; Antoine Henrot; Paolo Salani. - In: INTERFACES AND FREE BOUNDARIES. - ISSN 1463-9963. - STAMPA. - 16:(2014), pp. 215-241. [10.4171/IFB/318]
An overdetermined problem with non-constant boundary condition
BIANCHINI, CHIARA;SALANI, PAOLO
2014
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 problem, we prove existence and regularity of a solution. Moreover several geometric properties of the solution are shown.
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