Overdetermined problems in unbounded domains with Lipschitz singularities

  • Alberto Farina

    Université de Picardie Jules Verne, Amiens, France
  • Enrico Valdinoci

    Università di Roma Tor Vergata, Italy

Abstract

We study the overdetermined problem

where is a locally Lipschitz epigraph, that is on , with consisting in nonaccumulating, countably many points. We provide a geometric inequality that allows us to deduce geometric properties of the sets for which monotone solutions exist. In particular, if is a cone and either or and , then there exists no solution of

This answers a question raised by Juan Luis Vázquez.

Cite this article

Alberto Farina, Enrico Valdinoci, Overdetermined problems in unbounded domains with Lipschitz singularities. Rev. Mat. Iberoam. 26 (2010), no. 3, pp. 965–974

DOI 10.4171/RMI/623