Hopf-Lax-Oleinik-type formulas for viscosity solutions to some Hamilton-Jacobi equations (Q1775321)

This paper is a survey of results on Hopf-Lax-Oleinik type and explicit formulas of \[ \begin{aligned} u_t+H(t,u,Du)=0&\quad\text{in } \{t>0,x\in\mathbb{R}^n\},\\ u(0,x)=\phi(x)&\quad\text{on } \{t=0,x\in\mathbb{R}^n\}, \end{aligned} \] \noindent obtained by the author and collaborators in some recent papers. See for instance Adv. Math. Sci. Appl. 10, No. 1, 239--264 (2000; Zbl 0961.35026) and Vietnam J. Math. 26, No. 4, 385--389 (1998; Zbl 0967.35028).