Marino Belloni, Bernd Kawohl (2004)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the pseudo--laplacian, an anisotropic version of the -laplacian operator for . We study relevant properties of its first eigenfunction for finite and the limit problem as .
Francesca Da Lio, Annamaria Montanari (2006)
Annales de l'I.H.P. Analyse non linéaire
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Yifeng Yu (2009)
Annales de l'I.H.P. Analyse non linéaire
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Pierpaolo Soravia (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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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...
Krzysztof A. Topolski (2008)
Czechoslovak Mathematical Journal
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We consider the initial-boundary value problem for first order differential-functional equations. We present the `vanishing viscosity' method in order to obtain viscosity solutions. Our formulation includes problems with a retarded and deviated argument and differential-integral equations.