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arXiv · 2605.02345

Sharp regularity for a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms

Wentao Huo·Xiaofeng Jin·Lingwei Ma·Zhenqiu Zhang
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Abstract

We investigate the regularity of the viscosity solutions to a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms. To overcome the difficulty caused by the simultaneous presence of the general degenerate/singular gradient terms and Hamiltonian terms, we analyze the coupled interplay between the degeneracy/singularity law and the growth of Hamiltonian terms and establish lower regularity results. Finally, we obtain sharp interior $C^{1,\alpha}$ regularity estimates via a geometric tangential method.

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Wentao Huo, Xiaofeng Jin, Lingwei Ma, Zhenqiu Zhang. 2026-05-04. Sharp regularity for a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms. https://arxiv.org/abs/2605.02345

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