Calculus of Variations and Geometric Measure Theory
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M. Bardi - P. Mannucci

Comparison principles for equations of Monge-Ampère type in Carnot groups: a direct proof

created by bardi on 03 Feb 2009
modified on 15 Dec 2009


Published Paper

Inserted: 3 feb 2009
Last Updated: 15 dec 2009

Journal: Lect. Notes Semin. Interdiscip. Mat.
Volume: 7
Pages: 41-51
Year: 2008


We study fully nonlinear partial differential equations involving the determinant of the Hessian matrix of the unknown function with respect to a family of vector fields that generate a Carnot group. We prove a comparison theorem among viscosity sub- and supersolutions, for subsolutions uniformly convex with respect to the vector fields.

Keywords: Carnot groups, Viscosity solutions, Monge-Ampère equations, Subelliptic PDEs


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