Gilbarg-Serrin Equation and Lipschitz Regularity
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.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.