Displaying similar documents to “Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature”

Degenerate Eikonal equations with discontinuous refraction index

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...

Optimal regularity for the pseudo infinity Laplacian

Julio D. Rossi, Mariel Saez (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity Laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem.

On the smoothness of viscosity solutions of the prescribed Levi-curvature equation

Giovanna Citti, Ermanno Lanconelli, Annamaria Montanari (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper a C ∞ -regularity result for the strong viscosity solutions to the prescribed Levi-curvature equation is announced. As an application, starting from a result by Z. Slodkowski and G. Tomassini, the C ∞ -solvability of the Dirichlet problem related to the same equation is showed.