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arXiv · 2605.10369

Global $ C^{1}$ regularity for degenerate fully nonlinear elliptic equations

Jiangwen Wang·Feida Jiang
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Abstract

In this paper, we prove global $ C^{1}$ regularity for Dirichlet problem of a class of degenerate fully nonlinear elliptic equations on $ C^{2}$ domain. This corresponds to the boundary counterpart of the interior $ C^{1}$ regularity results by \cite{APPT22} and \cite{AN25}. By an example, we show that $ C^{1, \alpha}$ regularity of boundary datum is sharp within the scale of H\"{o}lder spaces. Furthermore, we also provide boundary $ C^{1, \beta}$ regularity for a class of singular fully nonlinear elliptic equations.

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Jiangwen Wang, Feida Jiang. 2026-05-11. Global $ C^{1}$ regularity for degenerate fully nonlinear elliptic equations. https://arxiv.org/abs/2605.10369

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