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arXiv · 2105.10906

Viscosity subsoltions of Hamilton-Jacobi equations and Invariant sets of contact Hamilton systems

Xiang Shu·Jun Yan·Kai Zhao
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Abstract

The objective of this paper is to present some results about viscosity subsolutions of the contact Hamiltonian-Jacobi equations on connected, closed manifold $M$ $$ H(x,\partial_x u,u)= 0, \quad x\in M. $$ Based on implicit variational principles introduced in [12,14], we focus on the monotonicity of the solution semigroups on viscosity subsolutions and the positive invariance of the epigraph for viscosity subsolutions. Besides, we show a similar consequence for strict viscosity subsolutions on $M$.

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Xiang Shu, Jun Yan, Kai Zhao. 2021-05-23. Viscosity subsoltions of Hamilton-Jacobi equations and Invariant sets of contact Hamilton systems. https://doi.org/10.1063/5.0078226

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