Intrinsic geometry and De Giorgi classes for certain anisotropic problems
The authors deal with nonlinear operators and functional classes modeled after the anisotropic Laplacian operator. We recall that anisotropic operators appear especially in Physics, when directional derivatives with distinct weights create distortions in the ambient space. The authors give a natural extension of the usual De Giorgi classes for functions in the anisotropic Sobolev spaces based on the intrinsic (parabolic) scaling proposed by DiBenedetto. Moreover, they prove that the anisotropic De Giorgi classes contain the quasi-minima \(u\) of any energy anisotropic functional.
scientific article; zbMATH DE number 6710660
scientific article