Author

Fanze Kong

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Preprint Sep 2026

Maximal Regularity and Existence for Superquadratic Parabolic Hamilton--Jacobi Equations: The Endpoint case

We establish interior maximal $L^{q_c}$-regularity for bounded strong solutions of $u_t-\Delta u+|Du|^\gamma=f$ in $\mathbb{T}^d\times(0,T)$, where $d\geq 2$, $\gamma>2$, and $q_c=(d+2)(\gamma-1)/\gamma$. The estimates are uniform for uniformly bounded families of solutions whose source terms range over a bounded, unif...

Fan-Ze Kong, Xiao-Yu Zeng · 0 citations

Preprint Aug 2026

Endpoint Maximal Regularity for Superquadratic Hamilton-Jacobi Equations and Applications to Ergodic Mean-field Games Systems

A celebrated conjecture of P.-L. Lions concerns maximal regularity for viscous Hamilton--Jacobi equations. In this paper, we study the endpoint case. We consider normalized strong solutions of $$-\Delta u+|Du|^\gamma=f$$ in $\mathbb T^d$, where $d\geq 2$, $\gamma>2$, and $f\in L^{q_c}(\mathbb T^d)$ with $q_c=d(\gamma-1...

Fan-Ze Kong · 0 citations

Preprint Aug 2026

Maximal Regularity of Superquadratic Hamilton-Jacobi Equations: The Endpoint Case in Lions'Conjecture

A celebrated conjecture of P.-L. Lions concerns maximal regularity for viscous Hamilton-Jacobi equations. In this paper, we study the endpoint case. We consider normalized strong solutions of $-\Delta u+|Du|^\gamma=f$ on $\mathbb T^d$, where $d\geq 2$, $\gamma>2$, and $f\in L^{q_c}(\mathbb T^d)$ with $q_c=d(\gamma-1)/\...

Fanze Kong · 0 citations