Asymptotic Lipschitz regularity of viscosity solutions of Hamilton-Jacobi equations

Xia Li; Lin Wang

Asymptotic Lipschitz regularity of viscosity solutions of Hamilton-Jacobi equations

Analysis of PDEs 2017-05-25 v1 Dynamical Systems

Authors: Xia Li , Lin Wang

Abstract

For each continuous initial data $\varphi(x)\in C(M,\mathbb{R})$ , we obtain the asymptotic Lipschitz regularity of the viscosity solution of the following evolutionary Hamilton-Jacobi equation with convex and coercive Hamiltonians: \partial_tu(x,t)+H(x,\partial_xu(x,t))=0, u(x,0)=\varphi(x).

Keywords

Hamilton-Jacobi equations viscosity solutions asymptotic Lipschitz regularity convex Hamiltonian coercive Hamiltonian

Cite

@article{arxiv.1705.08644,
  title  = {Asymptotic Lipschitz regularity of viscosity solutions of Hamilton-Jacobi equations},
  author = {Xia Li and Lin Wang},
  journal= {arXiv preprint arXiv:1705.08644},
  year   = {2017}
}

Comments

to appear in Proceedings of the AMS

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