Filomena De Filippis: Schauder estimates at nearly linear growth

Speaker
Filomena De Filippis, University of Parma

Abstract
Variational integrals at nearly linear growth appear in the theory of plasticity with logarithmic hardening, that is the borderline configuration between plasticity with power hardening and perfect plasticity. The related (very challenging) regularity theory for minima has been intensively developed over the last 25 years, see e.g. the work of Frehse & Seregin ’99, Fuchs & Mingione ’00, Bildhauer ’03, Beck & Schmidt ‘13, Beck & Bulícek & Gmeineder ’20, Di Marco & Marcellini ’20, Gmeineder & Kristensen ’22, De Filippis & Mingione ’23. In this respect, we will discuss an intrinsic approach to the theory of Schauder for general nonautonomous functionals at nearly linear growth that covers the most common model examples in the literature. From recent, joint work with Cristiana De Filippis (Parma), Peter Hästö (Helsinki), and Mirco Piccinini (Pisa).