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Abstract |
So-called Schauder estimates are a standard tool in the analysis of linear elliptic and parabolic PDEs. They had been originally proved by Hopf (1929, interior case), and by Schauder and Caccioppoli (1934, global estimates). Since then, several proofs were given (Campanato, Trudinger, Simon). The nonlinear case is a more recent achievement from the 80s (Giaquinta & Giusti, Ivert, J. Manfredi, Lieberman). All these classical results take place in the uniformly elliptic case. I will discuss progress in the nonuniformly elliptic one. |
