An A Priori Estimate for the Modulus of Continuity of a Generalized Solution of a Parabolic Equation of Divergent Form with Degeneracy

Abstract

We study parabolic equations of divergent form with degeneracy λ(x) with respect to the space variable. We establish an a priori estimate of the Hölder norm of generalized solutions. The problem is considered in parabolic cylinders having a special time dimension induced by the degeneracy λ(x).