Gilbarg-Serrin Equation and Lipschitz Regularity
Analysis of PDEs
2021-09-14 v3
Abstract
We discuss conditions for Lipschitz and C^1 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 C^1 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.
Keywords
Cite
@article{arxiv.2108.05764,
title = {Gilbarg-Serrin Equation and Lipschitz Regularity},
author = {Vladimir Maz'ya and Robert McOwen},
journal= {arXiv preprint arXiv:2108.05764},
year = {2021}
}
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15 pages