JournalsifbVol. 12, No. 3pp. 347–368

Cauchy problems for noncoercive Hamilton–Jacobi–Isaacs equations with discontinuous coefficients

  • Cecilia De Zan

    Università di Padova, Italy
  • Pierpaolo Soravia

    Università di Padova, Italy
Cauchy problems for noncoercive Hamilton–Jacobi–Isaacs equations with discontinuous coefficients cover
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Abstract

We study the Cauchy problem for a homogeneous and not necessarily coercive Hamilton–Jacobi–Isaacs equation with an x-dependent, piecewise continuous coefficient. We prove that under suitable assumptions there exists a unique and continuous viscosity solution. The result applies in particular to the Carnot–Carathéodory eikonal equation with discontinuous refraction index of a family of vector fields satisfying the Hörmander condition. Our results are also of interest in connection with geometric flows with discontinuous velocity in anisotropic media with a non-euclidian ambient space.

Cite this article

Cecilia De Zan, Pierpaolo Soravia, Cauchy problems for noncoercive Hamilton–Jacobi–Isaacs equations with discontinuous coefficients. Interfaces Free Bound. 12 (2010), no. 3, pp. 347–368

DOI 10.4171/IFB/238