Nonuniform ellipticity and related problemsLecture

by Dr Filomena De Filippis

Thursday Nov 5, 2026, 10:45 AM → 11:30 AM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Starting from classical elliptic regularity, this talk will present recent advances in Schauder theory for nonuniformly elliptic variational problems, focusing on anisotropic energies whose growth is arbitrarily close to linear. Such integrals arise in the theory of plasticity with logarithmic hardening, at the borderline between power hardening and perfect plasticity. The regularity of their minimizers has been extensively studied over the past decades. In the nonautonomous setting, a central question raised by Giaquinta, Modica and Souček in 1979 is whether Schauder theory is compatible with μ-ellipticity. I will discuss sharp regularity results addressing this question in the maximal nonuniformity range, together with insights into more general nonautonomous area-type integrals.

The talk is based on recent joint work with Cristiana De Filippis, Peter Hästö, and Mirco Piccinini.