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math.AP2025
Sketches of Nonuniformly Elliptic Schauder Theory
Cristiana De Filippis
Schauder theory is a basic tool in the study of elliptic and parabolic PDEs, asserting that solutions inherit the regularity of the coefficients. It plays a central role in establi…
math.AP2025
Partial regularity in nonlocal systems I
Cristiana De Filippis, Giuseppe Mingione, Simon Nowak
Solutions to nonlinear integro-differential systems are regular outside a negligible closed subset whose Hausdorff dimension can be explicitly bounded from above. This subset can b…