Degenerate Eikonal Equations with Discontinuous Refraction Index

  title={Degenerate Eikonal Equations with Discontinuous Refraction Index},
  author={Pierpaolo Soravia},
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… CONTINUE READING

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