Correspondence Between Renormalized and Entropy Solutions to the Parabolic Initial-Boundary Value Problem Involving Variable Exponents and Measure Data

Abstract

We study the initial-boundary value parabolic problem involving variable exponent under the generalized Leray-Lions conditions. We clarify the definitions of entropy and renormalized solutions to such parabolic problems, and we establish the equivalence between these definitions of entropy and renormalized solutions to the parabolic problems with the Leray-Lions operator and with measure data.