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

On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations

created by bardi on 01 Dec 2005
modified on 06 Sep 2007


Published Paper

Inserted: 1 dec 2005
Last Updated: 6 sep 2007

Journal: Commun. Pure Appl. Anal.
Volume: 5
Pages: 709-731
Year: 2006


We prove some comparison principles for viscosity solutions of fully nonlinear degenerate elliptic equations that satisfy conditions of partial non-degeneracy instead of the usual uniform ellipticity or strict monotonicity. These results are applied to the well-posedness of the Dirichlet problem under suitable conditions at the characteristic points of the boundary. The examples motivating the theory are operators of the form of sum of squares of vector fields plus a nonlinear first order Hamiltonian and the Pucci operator over the Heisenberg group.

Keywords: Viscosity solutions, subelliptic equations, Comparison principle, Pucci operators


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