An overdetermined problem with non constant boundary condition

Chiara Bianchini (1) , Antoine Henrot (2) , Paolo Salani (1)

1 Dipartimento di Matematica "Ulisse Dini"
2 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: Torsion problem; overdetermined problem; shape optimization

Domaines: Equations aux dérivées partielles [math.AP]

Chiara Bianchini, Antoine Henrot, Paolo Salani. An overdetermined problem with non constant boundary condition. Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications, 2014, 16, pp.215-241. ⟨10.4171/IFB/318⟩. ⟨hal-00790065⟩