卡诺群中不连续汉密尔顿-雅可比方程的 Monge 解决方案

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-08-01 DOI:10.1007/s00030-024-00983-y

Fares Essebei, Gianmarco Giovannardi, Simone Verzellesi

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引用次数: 0

摘要

本文在卡诺群的框架内研究了与非连续哈密顿相关的静态哈密顿-雅可比方程的 Monge 解。在证明连续环境中 Monge 解与粘性解的等价性之后，我们证明了 Dirichlet 问题的存在性和唯一性，以及比较原理和稳定性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Monge solutions for discontinuous Hamilton-Jacobi equations in Carnot groups

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Monge solutions for discontinuous Hamilton-Jacobi equations in Carnot groups

In this paper we study Monge solutions to stationary Hamilton–Jacobi equations associated to discontinuous Hamiltonians in the framework of Carnot groups. After showing the equivalence between Monge and viscosity solutions in the continuous setting, we prove existence and uniqueness for the Dirichlet problem, together with a comparison principle and a stability result.

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Nonlinear Differential Equations and Applications (NoDEA)

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