Viscosity solutions of discontinuous Hamilton–Jacobi equations

  • Bei Hu

    University of Notre Dame, USA
  • Xinfu Chen

    University of Pittsburgh, United States


We define viscosity solutions for the Hamilton-Jacobi equation ϕt=v(x,t)H(ϕ)\phi_t = v(x,t) H(\nabla \phi) in \BRN×(0,)\BR^N\times(0,\infty) where vv is positive and bounded measurable and HH is non-negative and Lipschitz continuous. Under certain assumptions, we establish the existence and uniqueness of Lipschitz continuous viscosity solutions. The uniqueness result holds in particular for those vv which are independent of tt and piecewise continuous with discontinuous sets consisting of finitely many smooth lower dimensional surfaces not tangent to each other at any point of their intersection.ets are determined by the solution of a disc packing problem.

Cite this article

Bei Hu, Xinfu Chen, Viscosity solutions of discontinuous Hamilton–Jacobi equations. Interfaces Free Bound. 10 (2008), no. 3, pp. 339–359

DOI 10.4171/IFB/192