Calculus of Variations and Geometric Measure Theory

P. Baroni - A. Di Castro - G. Palatucci

Intrinsic geometry and De Giorgi classes for certain anisotropic problems

created by palatucci on 29 Oct 2016
modified on 15 Nov 2018


Published Paper

Inserted: 29 oct 2016
Last Updated: 15 nov 2018

Journal: Discrete Contin. Dyn. Syst. - Series S
Volume: 10
Number: 4
Pages: 647--659
Year: 2017


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