Degenerate Eikonal equations with discontinuous refraction index
ESAIM: Control, Optimisation and Calculus of Variations, Volume 12 (2006) no. 2, pp. 216-230.

We study the Dirichlet boundary value problem for eikonal type equations of ray light propagation in an inhomogeneous medium with discontinuous refraction index. We prove a comparison principle that allows us to obtain existence and uniqueness of a continuous viscosity solution when the Lie algebra generated by the coefficients satisfies a Hörmander type condition. We require the refraction index to be piecewise continuous across Lipschitz hypersurfaces. The results characterize the value function of the generalized minimum time problem with discontinuous running cost.

DOI: 10.1051/cocv:2005033
Classification: 35A05,  35F30,  49L20,  49L25
Keywords: geometric optics, viscosity solutions, eikonal equation, minimum time problem, discontinuous coefficients
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     title = {Degenerate {Eikonal} equations with discontinuous refraction index},
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Soravia, Pierpaolo. Degenerate Eikonal equations with discontinuous refraction index. ESAIM: Control, Optimisation and Calculus of Variations, Volume 12 (2006) no. 2, pp. 216-230. doi : 10.1051/cocv:2005033. http://archive.numdam.org/articles/10.1051/cocv:2005033/

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