Four different lectures

1) Basic results from classical regularity theory

2) Aspects of Nonlinear Calderon-Zygmund

3) Aspects of Nonlinear Potential Theory

4) Non-uniformly elliptic problems

Oct 7: 11:00-11:50 AM at Benedum Hall G27

Oct 8: 11:00-11:50 AM at GSPH A522

Oct 9: 9:00-9:50 AM at Benedum Hall G27

Oct 10: 11:00-11:50 AM at GSPH A522

### Abstract or Additional Information

The aim of the course is to give a brief overview of recent progresses in the regularity theory of quasilinear and possibly degenerate equations and systems. The celebrated p-Laplacian operator provides a paramount model case. Major emphasis is put on how the regularity of solutions depends on that of the given data. This immediately leads to modern developments as those in Nonlinear Potential Theory, and Nonlinear Calderon-Zygmund theory, whose aims is to reproduce, in the case of nonlinear equations, results and estimates that are typical of the standard linear Potential Theory.

The course develops through four different lectures as follows:

1) Basic results from classical regularity theory

2) Aspects of Nonlinear Calderon-Zygmund

3) Aspects of Nonlinear Potential Theory

4) Non-uniformly elliptic problems