Inserted: 29 oct 2016
Last Updated: 15 nov 2018
Journal: Discrete Contin. Dyn. Syst. - Series S
We analyze a natural approach to the regularity of solutions of problems related to some anisotropic Laplacian operators, and a subsequent extension of the usual De Giorgi classes, by investigating the relation of the functions in such classes with the weak solutions to some anisotropic elliptic equations as well as with the quasi-minima of the corresponding functionals with anisotropic polynomial growth.
Keywords: anisotropic Sobolev spaces, Caccioppoli estimates, Anisotropic De Giorgi Classes