Displaying similar documents to “Smooth regularity for solutions of the Levi Monge-Ampère equation”

The Dirichlet problem for the degenerate Monge-Ampère equation.

Luis A. Caffarelli, Louis Nirenberg, Joel Spruck (1986)

Revista Matemática Iberoamericana

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Let Ω be a bounded convex domain in Rn with smooth, strictly convex boundary ∂Ω, i.e. the principal curvatures of ∂Ω are all positive. We study the problem of finding a convex function u in Ω such that: det (uij) = 0 in Ω u = φ given on ∂Ω.

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.

Levi-equation in higher dimensions

Zbginiew Slodkowski, Giuseppe Tomassini (1991)

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

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We announce some results concerning the Dirichlet problem for the Levi-equation in C n . We consider for the sake of simplicity the case n = 3 .