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We prove regularity results such as interior Lipschitz regularity and boundary continuity for the Cauchy–Dirichlet problem associated to a class of parabolic equations inspired by the evolutionary p -Laplacian, but extending it at a wide scale. We employ a regularization technique of viscosity-type that we find interesting in itself. [ABSTRACT FROM AUTHOR]

We consider solutions to singular parabolic equations with measurable dependence on the ( x , t ) variables and having on the right-hand side a measure satisfying a density condition. We prove that the less the measure is concentrated, the more the gradient is regular, in the Marcinkiewicz scale. We provide local estimates and recover some classic results. [ABSTRACT FROM AUTHOR]

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]

We consider a weak solution to the non-linear, parabolic systems of the form ut - div A( x, t, u, Du) = 0, where the vector field A satisfies a Dini-type continuity condition with respect to the variables ( x, t, u), and we prove a partial regularity result for such a solution. Moreover, we give an estimate of the size of the singular set of a solution in terms of a generalized parabolic Hausdorff measure associated to an appropriate modulus of continuity naturally associated to the coefficients of the system. [ABSTRACT FROM AUTHOR]