The intrinsic Hopf-Lax semigroup vs. The intrinsic slope

DOI10.1016/J.JMAA.2023.127051zbMath1518.37076arXiv2207.04486MaRDI QIDQ6404528

Publication date: 10 July 2022

Abstract: In this note, we introduce a natural notion of intrinsic Hopf-Lax semigroup in the context of the so-called intrinsically Lipschitz sections. The main aims are to prove the link between the intrinsic Hopf-Lax semigroup and the intrinsic slope and to show that the intrinsic Hopf-Lax semigroup is a subsolution of Hamilton-Jacobi type equality.

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05) Sub-Riemannian geometry (53C17) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Hamilton-Jacobi equations (35F21) PDEs on manifolds (35R01)

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