Author

Yifeng Yu

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Preprint Oct 2026

Pathological viscosity solutions of Hamilton--Jacobi equations

We construct a continuous function $u$ on the closed unit ball in $\mathbb{R}^4$ and a smooth autonomous Hamiltonian $H:\mathbb{R}^4\to[1,2]$ for which $u$ solves $H(Du)=c$ in the unit ball in the viscosity sense for every $c\in[1,2]$. This reveals a striking and distinctive pathology of viscosity solutions: a fixed fu...

H. V. Tran, Yi-Feng Yu · 0 citations

Preprint Sep 2026

$L^\infty$ Variational Approximation of the Aubry Set

Let $H\in C^\infty(\mathbb R^n\times\mathbb T^n)$ be a periodic Tonelli Hamiltonian with critical value $c$. For each $k\in\mathbb N$, let $u_k$ be the normalized minimizer of the variational functional introduced by Evans[7], \[ I_k[w]=\int_{\mathbb T^n} e^{kH(Dw,x)}\,dx, \qquad \int_{\mathbb T^n}w\,dx=0. \] If $u_\in...

H. V. Tran, Yi-Feng Yu · 0 citations