On the properties of infinty-harmonic functions and an application to capacitary convex rings

Electronic Journal of Differential Equations

关键词: Viscosity solutions;    boundary Harnack inequality;    infinity-Laplacian;    capacitary functions;    convex rings;   

DOI  :  

来源: DOAJ

【 摘 要 】

We study positive $infty$-harmonic functions in bounded domains. We use the theory of viscosity solutions in this work. We prove a boundary Harnack inequality and a comparison result for such functions near a flat portion of the boundary where they vanish. We also study $infty$-capacitary functions on convex rings. We show that the gradient satisfies a global maximum principle, it is nonvanishing outside a set of measure zero and the level sets are star-shaped.

【 授权许可】

Unknown