# Degenerate Eikonal equations with discontinuous refraction index

ESAIM: Control, Optimisation and Calculus of Variations (2006)

- Volume: 12, Issue: 2, page 216-230
- ISSN: 1292-8119

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topSoravia, Pierpaolo. "Degenerate Eikonal equations with discontinuous refraction index." ESAIM: Control, Optimisation and Calculus of Variations 12.2 (2006): 216-230. <http://eudml.org/doc/249679>.

@article{Soravia2006,

abstract = {
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.
},

author = {Soravia, Pierpaolo},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Geometric optics; viscosity solutions; eikonal equation; minimum time problem; discontinuous coefficients.; discontinuous coefficients; Dirichlet boundary value problem; ray light propagation; comparison principle},

language = {eng},

month = {3},

number = {2},

pages = {216-230},

publisher = {EDP Sciences},

title = {Degenerate Eikonal equations with discontinuous refraction index},

url = {http://eudml.org/doc/249679},

volume = {12},

year = {2006},

}

TY - JOUR

AU - Soravia, Pierpaolo

TI - Degenerate Eikonal equations with discontinuous refraction index

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2006/3//

PB - EDP Sciences

VL - 12

IS - 2

SP - 216

EP - 230

AB -
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.

LA - eng

KW - Geometric optics; viscosity solutions; eikonal equation; minimum time problem; discontinuous coefficients.; discontinuous coefficients; Dirichlet boundary value problem; ray light propagation; comparison principle

UR - http://eudml.org/doc/249679

ER -

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