Nonuniformly elliptic Schauder theory

2022/01/19 by De Filippis, Cristiana, Mingione, Giuseppe · 17 citations
#35J60 #49N60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.07369

Abstract

Local Schauder estimates hold in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic variational problems and elliptic equations are locally Hölder continuous, provided coefficients are locally Hölder continuous.

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• Schauder and Cordes–Nirenberg estimates for nonlocal elliptic equations with singular kernels
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