JournalsifbVol. 16, No. 2pp. 215–241

An overdetermined problem with non-constant boundary condition

  • Chiara Bianchini

    Università degli Studi di Firenze, Italy

  • Antoine Henrot

    Université de Lorraine, Vandoeuvre-les-Nancy, France

  • Paolo Salani

    Università degli Studi di Firenze, Italy
An overdetermined problem with non-constant boundary condition cover
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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.

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

DOI 10.4171/IFB/318