Characterization of stadium-like domains via boundary value problems for the infinity Laplacian. (March 2016) - Crasta, Graziano; Fragalà, Ilaria
Abstract: We give a complete characterization, as "stadium-like domains", of convex subsets Ω of R n where a solution exists to Serrin-type overdetermined boundary value problems in which the operator is either the infinity Laplacian or its normalized version. In case of the not-normalized operator, our results extend those obtained in a previous work (where the problem was solved under some geometrical restrictions on Ω ), while in the case of the normalized operator they are new. In the normalized case, we also show that stadium-like domains are precisely the unique convex sets in R n where the solution to a Dirichlet problem is of class C 1, 1 ( Ω ) .