The intrinsic Hopf-Lax semigroup vs. The intrinsic slope
Daniela Di Donato
TL;DR
This paper introduces an intrinsic Hopf-Lax semigroup for intrinsically Lipschitz sections, establishing its connection to the intrinsic slope and its role as a subsolution to Hamilton-Jacobi equations.
Contribution
It defines a new intrinsic Hopf-Lax semigroup and explores its relationship with the intrinsic slope and Hamilton-Jacobi subsolutions.
Findings
Established the link between the intrinsic Hopf-Lax semigroup and the intrinsic slope.
Proved that the intrinsic Hopf-Lax semigroup is a subsolution of Hamilton-Jacobi type equations.
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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Optimization and Variational Analysis · Stochastic processes and financial applications