Hölder continuity of singular parabolic equations with variable nonlinearity

Abstract

In this paper we obtain the local Hölder regularity of the weak solutions for singular parabolic equations with variable exponents. The proof is based on DiBenedetto’s technique called intrinsic scaling; by choosing an appropriate geometry one can deduce energy and logarithmic estimates from which one can implement an iterative method to obtain the regularity result.

Keywords

• nonlinear parabolic equations
• singular equations
• variable nonlinearity
• regularity of solutions
• primary 35k55, 35k67
• secondary 35b65