Harnack inequality for a class of functionals with non-standard growth via De Giorgi’s method

Abstract

We study the regularity theory of quasi-minimizers of functionals with Lp⁢(⋅)⁢log⁡L{L^{p(\,\cdot\,)}\log L}-growth. In particular, we prove the Harnack inequality and, in addition, the local boundedness and the Hölder continuity of the quasi-minimizers. We directly prove our results via De Giorgi’s method.

Keywords

• non-standard growth
• quasi-minimizer
• hölder continuity
• harnack inequality, variable exponent
• 35j92
• 35j20
• 35b65