Harnack inequality and an asymptotic mean-value property for the Finsler infinity-Laplacian
The study of anisotropic problems in calculus of variations goes all the way back to at least the seminal work by George Wullf who studied the mathematical theory of crystals and minimization of surface energies. Closely related to this is the anisotropic Laplacian (or Finsler Laplacian). The Finsler-Minkowski norms lead to natural generalizations of many classical elliptic operators, and this has motivated the study of elliptic operators defined with respect to Finsler-Minkowski norms. In this paper, the authors prove a Harnack inequality for nonnegative viscosity supersolutions of nonhomogeneous equations associated with normalized Finsler infinity-Laplace operators. Viscosity solutions to homogeneous equations are also characterized via an asymptotic mean-value property, understood in a viscosity sense.
scientific article; zbMATH DE number 7367617
scientific article