Solvability of Parabolic Regularity problem in Lebesgue spaces

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The main objective of this proposal is to meet this need and develop novel mathematical ideas for parabolic partial differential equations with rough coefficients which occur frequently in real applications (such as physics and engineering).In recent years substantial progress has been achieved in our understanding of partial differential equations with rough coefficients and associated boundary value problems. The motivation to study equations with rough (or low regularity) coefficients is twofold. In many "real life" models, such as in materials science, the coefficients can be discontinuous (for example modelling impurities in the materials or cracks).The proposal addresses one aspect from wide field of open problems that concerns the Regularity problem for these equations.