Special Session 48: Recent Advances in Nonlinear PDEs and Inverse Problems

Nonlocal Partial Regularity
Cristiana Filippis
University of Parma
Italy
Co-Author(s):    Giuseppe Mingione, Simon Nowak
Abstract:
The failure of De Giorgi-Nash theory in vectorial problems opens to the study of partial regularity, namely smoothness of solutions outside a negligible, singular set. This is a classical phenomenon for systems and harmonic maps. I'll give an account of recent advances on nonlinear integro-differential systems, with emphasis on the structure and size of the singular set of solutions. From recent, joint work with Giuseppe Mingione (Parma) and Simon Nowak (Bielefeld).