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Explore a 47-minute lecture by Cristiana De Filippis on µ-ellipticity and nonautonomous integrals, presented at the Workshop on "Degenerate and Singular PDEs" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the concept of µ-ellipticity, which characterizes certain degenerate forms of ellipticity found in convex integrals with linear or nearly linear growth, such as the area integral or iterated logarithmic model. Learn about the historical development of regularity theory from classical work by Bombieri, De Giorgi, Miranda, Ladyzhenskaya, Ural'tseva, Frehse, and Seregin to later advancements in anisotropic cases by Bildhauer, Fuchs, Mingione, Beck, Schmidt, Gmeineder, and Kristensen. Discover how traditional approaches fail with nondifferentiable components and how recent breakthroughs by De Filippis and Mingione established Schauder theory for specific anisotropic, nonautonomous functionals with Hölder continuous coefficients. Gain insights into the latest progress on Schauder theory for anisotropic problems with growth approaching linear within maximal nonuniformity range, along with sharp results on more general nonautonomous area-type integrals, based on joint work with Filomena De Filippis, Giuseppe Mingione, and Mirco Piccinini.
