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. 965–974DOI 10.4171/RMI/623