Solvability of Parabolic Regularity problem in Lebesgue spaces

这一建议的主要目的就是为了满足这一需要，并为实际应用(如物理和工程)中经常出现的具有粗糙系数的抛物型偏微分方程求出新的数学思想。近年来，我们对具有粗糙系数的偏微分方程组及其相关边值问题的理解取得了实质性的进展。研究具有粗糙(或低正则性)系数的方程的动机是双重的。在许多“现实生活”模型中，例如在材料科学中，系数可能是不连续的(例如，对材料中的杂质或裂纹进行建模)。该建议从广泛的开放问题领域解决了与这些方程的正则性问题有关的一个方面。

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.