On and beyond propagation of singularities of viscosity solutions

Cannarsa, Piermarco; Cheng, Wei

doi:10.48550/arxiv.1805.11583

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2021

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“…The uniformness of such 0 holds because of uniform conditions (L1)-(L3) in [4] . In [5], they ask the following problem :…”

Section: Introductionmentioning

confidence: 99%

Global propagation of singularities for discounted Hamilton-Jacobi equations

Hong¹,

Zhao²

2021

Preprint

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The main purpose of this paper is to study the global propagation of singularities of viscosity solution to discounted Hamilton-Jacobi equationWe reduce the problem for equation (HJ ) into that for a time-dependent evolutionary Hamilton-Jacobi equation. We proved that the singularities of the viscosity solution of (HJ ) propagate along locally Lipschitz singular characteristics which can extend to +∞. We also obtained the homotopy equivalence between the singular set and the complement of associated the Aubry set with respect to the viscosity solution of equation (HJ ).

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“…The uniformness of such 0 holds because of uniform conditions (L1)-(L3) in [4] . In [5], they ask the following problem :…”

Section: Introductionmentioning

confidence: 99%