Characterization of stadium-like domains via boundary value problems for the infinity Laplacian. (March 2016)

• Record Type: Journal Article
• Authors: Crasta, Graziano; Fragalà, Ilaria
• Is Part Of: Nonlinear analysis. Volume 133(2016)
• Page Start: 228
• Page End: 249
• Publication Date: 2016-03
• Subjects: primary 35N25 -- secondary 49K30 35J70 49K20; Boundary value problems -- Overdetermined problems -- Infinity Laplacian -- Viscosity solutions -- Regularity -- Semiconcavity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.12.007
• Languages: English
• ISSNs: 0362-546X

Abstract

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 ) .