Author

Zhenhu Zhao

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Preprint Aug 2026

Optimal Weighted $L^2$ Hessian Estimates for Parabolic Equations under General Diffusion Marginals

We study weighted $L^2$ Hessian estimates for parabolic terminal equations under diffusion marginals. The reference diffusion determines the norm, and its generator may have different principal coefficients from the PDE. We characterize the limiting optimal Hessian constant uniformly over shrinking subintervals of a fi...

Jihao Long, Zhenhu Zhao · 0 citations

Preprint Aug 2026

Optimal Weighted \texorpdfstring{$L^2$}{L2} Hessian Estimates for Parabolic Equations: General Diffusion and Coefficient Mismatch

We study weighted $L^2$ Hessian estimates under diffusion marginals, allowing the equation's principal matrix to be chosen independently. For regular uniformly elliptic coefficients, bounded reference drift and compactly supported doubling initial laws, the optimal large-damping constant on the full interval is the max...

Jihao Long, Zhenhu Zhao · 0 citations

Preprint Aug 2026

Fully nonlinear parabolic equations under a fixed reference diffusion:weighted $L^2$ Hessian estimates and well-posedness

We develop a fixed-reference weighted $L^2$ theory for terminal-value fully nonlinear parabolic equations. A prescribed uniformly elliptic diffusion starting from a point determines both the linear reference operator and a space--time occupation measure; time weights of order $\alpha$ accommodate the point-start singul...

Jihao Long, Zhenhu Zhao · 0 citations