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

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arxiv 2105.10906 v1 pith:BTC6EYVM submitted 2021-05-23 math.DS math.AP

Xiang Shu , Jun Yan , Kai Zhao This is my paper · ORCID
classification math.DSmath.AP
keywords viscositysubsolutionscontactequationsbesidesclosedconnectedconsequence
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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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