Author

Bin Zhou

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Preprint Oct 2026

Global H\"older estimates for linearized Monge-Amp\`ere equations in divergence form with applications to dual semigeostrophic equations and periodic homogenization

We establish interior and global H\"older estimates for linearized Monge-Amp\`ere equations in divergence form in all dimensions $n\geq 3$, when the Hessian determinant of the convex Monge-Amp\`ere potential is bounded above and below by positive constants and the vector field on the right-hand side is bounded. The est...

Guo-Qing Cui, Chong Gu, N. Q. Le et al. · 3 citations

Preprint Aug 2026

Interior $C^{1,\alpha}$ estimates for the linearized Monge--Amp\`ere equation in two dimensions

We prove an interior $C^{1,\alpha}$ estimate for solutions of the homogeneous linearized Monge--Amp\`ere equation in dimension two under the assumption \[ 0<\lambda\leq \det D^2\varphi\leq\Lambda<+\infty. \] No continuity assumption on the Monge--Amp\`ere density is required. Our result is an affine-invariant analogue...

Ling Wang, Bin Zhou · 1 citation