Degenerate Eikonal equations with discontinuous refraction index
Università degli Studi di Padova,
Dipartimento di Matematica Pura e Applicata,
via Belzoni, 7, 35131 Padova, Italy; firstname.lastname@example.org
Revised: 28 February 2005
Revised: 7 March 2005
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.
Mathematics Subject Classification: 35A05 / 35F30 / 49L20 / 49L25
Key words: Geometric optics / viscosity solutions / eikonal equation / minimum time problem / discontinuous coefficients.
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