Seminar Analysis: Lorenzo Brasco (Aix-Marseille Université & University of Ferrara)

Regularity issues for some nonlocal and nonlinear elliptic equations

In this talk, I will review some regularity results for weak solutions of nonlocal variants of the p-Laplace equation. The model case is given by the Euler-Lagrange equation of an Aronszajn–Gagliardo–Slobodeckij seminorm. In particular, I will present a higher differentiability result for solutions, recently obtained in collaboration with Erik Lindgren (KTH). I will also discuss some connections of these equations to an Optimal Transport problem with congestion effects.

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