Author

Bao-Yue Yu

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Preprint Oct 2026

Sharp Hessian integrability for the planar Monge--Amp\`ere equation

We determine the optimal local integrability of the Hessian for planar convex Alexandrov solutions satisfying $$ \lambda\,dx\leq\mu_u\leq\lambda^{-1}\,dx, \qquad 0<\lambda<1. $$ The distributional Hessian satisfies the sharp endpoint estimate $$ D^2u\in L_{\mathrm{loc}}^{P,\infty}, \qquad P=\frac{1+\lambda}{1-\lambda}....

Xiao-Rui Lu, Jin Yan, Bao-Yue Yu et al. · 0 citations

Preprint Aug 2026

Liouville Rigidity and Universal Spacelikeness Estimates for a Lorentzian Prescribed Mean Curvature Equation

We prove a Liouville theorem for nonnegative entire strictly spacelike solutions of \[ \operatorname{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right)+u^p=0 \qquad\text{in }\mathbb R^n. \] If $n=2$ and $p\geqslant1$, or if $n\geqslant3$ and $1\leqslant p\leqslant\frac{n+2}{n-2}$, every nonnegative $C^2$ solution...

Xi-nan Ma, Tian Wu, Wang-Zhe Wu et al. · 0 citations

Preprint Aug 2026

Liouville Rigidity and Universal Spacelikeness Estimates for a Lorentzian Prescribed Mean Curvature Equation

We prove a Liouville theorem for nonnegative entire strictly spacelike solutions of \[ \operatorname{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right)+u^p=0 \qquad\text{in }\mathbb R^n. \] If $n=2$ and $p\geqslant1$, or if $n\geqslant3$ and $1\leqslant p<\frac{n+2}{n-2}$, every nonnegative $C^2$ solution satisfyi...

Xi-nan Ma, Tian Wu, Wangzhe Wu et al. · 0 citations