Gilbarg-Serrin Equation and Lipschitz Regularity

2021/08/12 by Maz'ya, Vladimir, McOwen, Robert
#35B40 (Secondary) #35B45 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.05764

Abstract

We discuss conditions for Lipschitz and C¹ regularity for a uniformly elliptic equation in divergence form with coefficients that were introduced by Gilbarg & Serrin. In particular, we find cases where Lipschitz or C¹ regularity holds but the coefficients are not Dini continuous, or do not even have Dini mean oscillation. The form of the coefficients also enables us to obtain specific conditions and examples for which there exists a weak solution that is not Lipschitz continuous.

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