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Daily Overview |
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RAR2: Recent advances in regularity theory for PDEs Location: M628 Session Chair: Simon Nowak Session Chair: Marvin Weidner | |
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Nonlocal Partial Regularity University of Parma, Italy 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 a negligible closed subset, called the singular set. In some cases, Hausdorff dimension estimates for this set can also be obtained. In general, the singular set is non-empty. This theory is classical, originating in the work of Giusti–Miranda and Morrey, and 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 at providing some basic general tools for proving so-called epsilon-regularity theorems in nonlocal settings. Based on recent joint work with Cristiana De Filippis (Parma) and Simon Nowak (Bielefeld); see also our survey paper in Discrete and Continuous Dynamical Systems 57 (2026). | |
