Rubio de Francia extrapolation theorem and related topics in the theory of elliptic and parabolic equations. A survey

This is a brief overview of the history of the Sobolev mixed norm theory of linear elliptic and parabolic equations and the recent development in this theory based on the Rubio de Francia extrapolation theorem. A self contained proof of this theorem along with other relevant tools of Real Analysis are also presented as well as an application to mixed norm estimates for fully nonlinear equations.