Regularity for elliptic equations under minimal assumptions

Elliptic PDEs are ubiquitous in Mathematics and Sciences. A very important  topic concerning Elliptic PDEs is the regularity of solutions. We will review some regularity results for linear and quasilinear uniformly  elliptic equations. The main focus will be on the  inimal assumptions we need in order to obtain a given degree of smoothness for the generalized solutions.