| Abstract: |
| The theory of partial regularity for elliptic systems replaces the classical De Giorgi-Nash-Moser theory for scalar equations, asserting that solutions are regular outside of an in general non-empty negligible closed subset called the singular set. The local theory was initiated by Giusti \& Miranda and Morrey, in turn relying on De Giorgi`s seminal ideas in the context of minimal surfaces. I will present several extensions of the classical local partial regularity theory to nonlinear integro-differential systems along with some general tools for proving $\varepsilon$-regularity theorems in nonlocal settings. This is joint work with Cristiana De Filippis and Giuseppe Mingione (Parma). |
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