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Abstract: We consider parabolic equations of the type having a Radon measure on the right-hand side and prove fractional integrability and differentiability results of Calderón–Zygmund type for weak solutions. We extend some of the integrability results for elliptic equations achieved by G. Mingione (2007) to the parabolic setting and locally recover the integrability results of L. Boccardo, A. DallʼAglio, T. Gallouët, and L. Orsina (1997) in . [Copyright &y& Elsevier]

Abstract: For local minimizers of quasiconvex integral functionals of the type with growth in the class , where is a given obstacle function, we show estimates of Calderón–Zygmund type, i.e. for any , provided that the modulus of continuity ω of the exponent function p satisfies the condition [Copyright &y& Elsevier]