Journal
INTERFACES AND FREE BOUNDARIES
Volume 12, Issue 3, Pages 347-368Publisher
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/IFB/238
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- MIUR
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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-Caratheodory eikonal equation with discontinuous refraction index of a family of vector fields satisfying the Hormander condition. Our results are also of interest in connection with geometric flows with discontinuous velocity in anisotropic media with a non-euclidian ambient space.
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