Author

Zong-Yuan Li

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Preprint Sep 2026

On the $W^{2,p}$ solvability for mixed boundary value problems

We establish global $W^{2,p}$ solvability for the Poisson equation with mixed Dirichlet--Neumann boundary conditions in two classes of domains in all dimensions $n\geq 2$. For $C^{1,\alpha}$ domains with a Reifenbeg flat interface, we obtain the optimal range $11-1/p$. For Lipschitz polyhedra with facewise boundary dec...

Rohit Khandelwal, Zong-Yuan Li · 0 citations

Preprint Sep 2026

On one-space dimensional parabolic equations with measurable coefficients: Sobolev estimates and the Alexandrov maximum principle

Let $0<\kappa<1$ and set $p_+=2/(1-\kappa)$ and $p_-=2/(1+\kappa)$. We construct a coefficient $\kappa\leq a\leq\kappa^{-1}$, smooth outside a compact set of Lebesgue measure zero, for which the $W^{1,2}_{p_+}$ estimate fails for the one-space dimensional nondivergence form parabolic equation. The corresponding solutio...

Hong-Jie Dong, Zong-Yuan Li · 0 citations