Flux-limited solutions and state constraints for quasi-convex   Hamilton-Jacobi equations
  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. 
Jessica Guerand
math.AP