Year: 2026
Type: preprint
Abstract: The sufficient conditions of Ladyzhenskaya \& Ural'tseva \cite{lu70} for interior gradient estimates in nonuniformly elliptic problems are found to be also necessary. Specifically, nonparametric minimal surfaces exhibit the maximal nonuniformity rate compatible with the local Lipschitz regularity of solutions, and the classical theory of Finn \cite{fin54} and Bombieri \& De Giorgi \& Miranda \cite{bdm69} doesn't extend beyond Bernstein genre $2$.
Source: arXiv (Cornell University)
Author: De Filippis, Cristiana
Institution: University of Parma
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204903228