Characterization of stadium-like domains via boundary value problems for the infinity Laplacian

摘要

We give a complete characterization, as "stadium-like domains", of convex subsets Omega 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 Omega), 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,C-1(Omega). (C) 2015 Elsevier Ltd. All rights reserved.