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

Jessica Guerand

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arXiv · 1607.03996

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

Jessica Guerand

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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.

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Jessica Guerand. 2016-07-14. Flux-limited solutions and state constraints for quasi-convex Hamilton-Jacobi equations. https://arxiv.org/abs/1607.03996

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