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arXiv · 1810.04487

Global $C^{1+α,\frac{1+α}{2}}$ regularity on the linearized parabolic Monge-Amp$\grave{e}$re equation

Lin Tang·Qian Zhang
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Abstract

In this paper, we establish global $C^{1+α,\frac{1+α}{2}}$ estimates for solutions of the linearized parabolic Monge-Amp$\grave{e}$re equation $$\mathcal{L}_ϕu(x,t):=-u_t\,\mathrm{det}D^2ϕ(x)+\mathrm{tr}[Φ(x) D^2 u]=f(x,t)$$ under appropriate conditions on the domain, Monge-Amp$\grave{e}$re measures, boundary data and $f$, where $Φ:=\mathrm{det}(D^2ϕ)(D^2ϕ)^{-1}$ is the cofactor of the Hessian of $D^2ϕ$.

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Lin Tang, Qian Zhang. 2018-10-10. Global $C^{1+α,\frac{1+α}{2}}$ regularity on the linearized parabolic Monge-Amp$\grave{e}$re equation. https://arxiv.org/abs/1810.04487

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