Flux-limited solutions and state constraints for quasi-convex Hamilton-Jacobi equations

Abstract

Imbert and Monneau proved that Soner's formulation of state constraint problems on a bounded interval is equivalent to the so-called flux-limited formulation they introduced recently. In the multidimensional setting, we show this result for a general ${\mathcal{C}}^1$ bounded open set of ${\mathbb{R}}^d$ and obtain the result in the stationary and the evolution type cases.

16 pages