Author

Xu-Shan Tu

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Preprint Oct 2026

Quantitative homogenization of Monge-Amp\`ere equations in periodic media

Let $u^\varepsilon$ and $u$ be the convex solutions of \[ \det D^2u^\varepsilon=F(x,x/\varepsilon),\qquad \det D^2u=\overline F(x) \] on a bounded convex domain $\Omega$, with the same Dirichlet data. Here, $F$ is uniformly positive and periodic in its second variable, and $\overline F(x)=\int_{\mathbb T^n}F(x,y)\,dy$....

Tian-Ling Jin, Yan-Yan Li, Hung V. Tran et al. · 0 citations

Preprint Aug 2026

Optimal regularity and fine asymptotics for very fast diffusion equations in bounded domains

We prove the optimal global regularity of admissible solutions to a transformed very fast diffusion equation in the range $-1<p<0$, posed on smooth bounded domains with zero Dirichlet boundary data and initial data comparable to the distance function. More precisely, we establish existence and uniqueness and show that...

Tian-Ling Jin, Xushan Tu, Jingang Xiong et al. · 0 citations