A Survey of Hopf-Lax Formulas and Quasiconvexity in PDEs

This is a short survey of recent results obtained by the author and collaborators primarily on Hopf-Lax formulas for Hamilton-Jacobi equations and obstacle problems. The initiation of the use of quasiconvex (i.e., level convex) functions in $L^\infty$ control and differential games led to such formulas and is briefly reviewed. Dedicated to the memory of Academician A. I. Subbotin.