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.
Cite this article
Chiara Bianchini, Antoine Henrot, Paolo Salani, An overdetermined problem with non-constant boundary condition. Interfaces Free Bound. 16 (2014), no. 2, pp. 215–241