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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 · 0 citations

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