Calderon-Zygmund regularity estimates for weak solutions of degenerate elliptic equations.
This talk reports several results on Sobolev regularity theory of Calderon-Zygmund type for weak solutions of elliptic equations in divergence form with degenerate, singular coefficients. We start with a class of linear equations of divergence form in which the coefficient matrix behaves as some weight function in some Muckenhoupt class of weights. Sufficient conditions on coefficients will be given to ensure suitable weighted Calderon-Zygmund regularity type estimates for weak solutions. An example will be discussed to show the necessity of our conditions. An extension of this result to nonlinear equations with two weighted estimates will be also discussed. A special case for which the coefficient matrices are degenerate or singular in one variable direction will be also investigated. The results mentioned are based on the papers: arXiv:1702.08622, arXiv:1612.07371, arXiv:1612.05583.