Degenerate Eikonal Equations with Discontinuous Refraction Index

@inproceedings{Soravia2006DegenerateEE,
  title={Degenerate Eikonal Equations with Discontinuous Refraction Index},
  author={Pierpaolo Soravia},
  year={2006}
}
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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References

Publications referenced by this paper.
Showing 1-10 of 22 references

Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian

  • P. Soravia
  • Indiana Univ. Math. J. 51
  • 2002
Highly Influential
10 Excerpts

Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

  • M. Bardi, I. Capuzzo-Dolcetta
  • Birkhäuser
  • 1997
Highly Influential
4 Excerpts

Solutions de viscosité des équations de Hamilton-Jacobi

  • G. Barles
  • Springer-Verlag
  • 1994
Highly Influential
4 Excerpts

Discontinuous viscosity solutions to Dirichlet problems for Hamilton-Jacobi equations with convex hamiltonians

  • P. Soravia
  • Commun. Partial Diff. Equations 18
  • 1993
Highly Influential
2 Excerpts

Hamilton-Jacobi equations with a singular boundary condition on a free boundary and applications to differential games

  • M. Bardi, P. Soravia
  • Trans. Amer. Math. Soc. 325
  • 1991
Highly Influential
2 Excerpts

Optimality principles and uniqueness for Bellman equations of unbounded control problems with discontinuous running cost

  • M. Garavello, P. Soravia
  • Nonlin. Diff. Equations Appl. 11
  • 2004
1 Excerpt

Hamilton-Jacobi equations with measurable dependence on the state variable

  • F. Camilli, A. Siconolfi
  • Adv. Differential Equations 8
  • 2003
3 Excerpts

Extending viscosity solutions to eikonal equations with discontinuous spatial dependence

  • D. N. Ostrov
  • Nonlinear Anal. TMA 42
  • 2000

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