Events for 01/21/2025 from all calendars
Nonlinear Partial Differential Equations
Time: 09:00AM - 10:00AM
Location: Zoom
Speaker: Cristiana De Filippis, University of Parma
Title: mu- ellipticity and nonautonomous integrals
Abstract: mu-ellipticity describes certain degenerate forms of ellipticity, typical of convex integrals at linear, or nearly linear growth such as the area integral, or the iterated logarithmic model. The regularity of solutions to autonomous or totally differentiable problems is classical after Bombieri and De Giorgi and Miranda, Ladyzhenskaya and Ural’tseva and Frehse and Seregin. The anisotropic case is a later achievement of Bildhauer, Fuchs and Mingione, Beck and Schmidt and Gmeineder and Kristensen, that provided a complete partial and full regularity theory. However, all the approaches developed so far break down in presence of nondifferentiable ingredients. In particular, Schauder theory for certain significant anisotropic, nonautonomous functionals with Hölder continuous coefficients was only recently obtained by Mingione and myself. I will give an overview of the latest progress on the validity of Schauder theory for anisotropic problems whose growth is arbitrarily close to linear within the maximal nonuniformity range, and discuss sharp results and deep insights on more general nonautonomous area type integrals. From recent, joint work with Filomena De Filippis (Parma), Giuseppe Mingione (Parma), and Mirco Piccinini (Pisa).