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Seminario Dottorato: A Viscosity approach to Monge-Ampere type PDEs

Wednesday 18 May 2011 - Marco Cirant

ARGOMENTI: Seminari Dottorato

SEMINARIO DOTTORATO
Wednesday 18 May 2011 h. 14:30, room 2BC30
Marco Cirant (Dip. Mat.)
"A Viscosity approach to Monge-Ampere type PDEs"

-Abstract
In this introductory talk we present some results of existence and uniqueness of solutions to the Dirichlet problem for the prescribed gaussian curvature equation, a Monge-Ampere type equation arising in differential geometry.
We implement the modern tools of viscosity theory, combined with new ideas of Harvey and Lawson; our point of view is also based upon Krylov's language of elliptic branches.
Our case study will be the homogeneous equation, i.e. when the curvature is identically zero, for which we outline the proof of existence and uniqueness of a convex solution (in a weak sense). Then, we sketch how to generalize these kind of results to the non-homogeneous equation and show some open problems related to curvature equations of more general form.

Rif. int. C. Marastoni, T. Vargiolu

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