Comparison principles and Dirichlet problem for fully nonlinear degenerate equations of Monge–Ampère type
-
Martino Bardi
and
Paola Mannucci
Abstract.
We study fully nonlinear
partial differential equations of Monge–Ampère type involving the derivatives with respect to a family 
of vector fields. The main result is a comparison principle among viscosity subsolutions, convex with respect to , and viscosity supersolutions (in a weaker sense than usual), which implies the uniqueness of solution to the Dirichlet problem. Its assumptions include the equation of prescribed horizontal Gauss curvature in Carnot groups. By the Perron method we also prove the existence of a solution either under a growth condition of the nonlinearity with respect to the gradient of the solution, or assuming the existence of a subsolution attaining continuously the boundary data, therefore generalizing some classical result for Euclidean Monge–Ampère equations.
© 2013 by Walter de Gruyter Berlin Boston
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- The space of linear maps into a Grassmann manifold
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- Comparison principles and Dirichlet problem for fully nonlinear degenerate equations of Monge–Ampère type
Articles in the same Issue
- Masthead
- Continuity of homomorphisms into power-associative complete normed algebras
- The connection problem associated with a Selberg type integral and the q-Racah polynomials
- The space of linear maps into a Grassmann manifold
- The integral cohomology of configuration spaces of pairs of points in real projective spaces
- The tree of irreducible numerical semigroups with fixed Frobenius number
- The topological decomposition of inverse limits of iterated wreath products of finite Abelian groups
- Comparison principles and Dirichlet problem for fully nonlinear degenerate equations of Monge–Ampère type
