Partial regularity in nonlocal problems
A talk in the Nonlocal Equations: Analysis and Numerics series by
Giuseppe Mingione from Parma
| Abstract: | The theory of partial regular regularity for elliptic systems replaces the
classical De Giorgi-Nash-Moser one for scalar equations asserting that solutions are regular outside a negligible closed subset called the singular
set. Eventually, Hausdorff dimension estimates on such a set can be given.
The singular set is in general non-empty. The theory is classical, started
by Giusti $\&$ Miranda and Morrey, in turn relying on De Giorgi’s seminal
ideas for minimal surfaces. I shall present a few results aimed at extending
the classical, local partial regularity theory to nonlinear integrodifferential systems and to provide a few basic, general tools in order to prove
so called epsilon-regularity theorems in general non-local settings. From
recent, joint work with Cristiana De Filippis (Parma) and Simon Nowak
(Bielefeld). Within the CRC this talk is associated to the project(s): A7 |