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Displaying similar documents to “Extension of solutions for Monge-Ampère equations of hyperbolic type”

Monge-Ampère equations and surfaces with negative Gaussian curvature

Mikio Tsuji (1997)

Banach Center Publications

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In [24], we studied the singularities of solutions of Monge-Ampère equations of hyperbolic type. Then we saw that the singularities of solutions do not coincide with the singularities of solution surfaces. In this note we first study the singularities of solution surfaces. Next, as the applications, we consider the singularities of surfaces with negative Gaussian curvature. Our problems are as follows: 1) What kinds of singularities may appear?, and 2) How can we extend the surfaces...

Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions

Dmitri V. Alekseevsky, Ricardo Alonso-Blanco, Gianni Manno, Fabrizio Pugliese (2012)

Annales de l’institut Fourier

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We study the geometry of multidimensional scalar 2 n d order PDEs (i.e. PDEs with n independent variables), viewed as hypersurfaces ℰ in the Lagrangian Grassmann bundle M ( 1 ) over a ( 2 n + 1 ) -dimensional contact manifold ( M , 𝒞 ) . We develop the theory of characteristics of ℰ in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of ℰ . After specializing such results to general...