In this paper we prove comparison principles between viscosity semicontinuous sub- and supersolutions of the generalized Dirichlet problem (in the sense of viscosity solutions) for the Levi Monge-Ampère equation. As a consequence of this result and of the Perron's method we get the existence of a continuous solution of the Dirichlet problem related to the prescribed Levi curvature equation under suitable assumptions on the boundary data and on the Levi curvature of the domain. We also show that such a solution is Lipschitz continuous by building Lipschitz continuous barriers and by applying a weak Bernstein method.

Existence and Uniqueness of Lipschitz Continuous Graphs with Prescribed Levi Curvature / F. Da Lio; A. Montanari. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 23:(2006), pp. 1-28. [10.1016/j.anihpc.2004.10.006]

Existence and Uniqueness of Lipschitz Continuous Graphs with Prescribed Levi Curvature

MONTANARI, ANNAMARIA
2006

Abstract

In this paper we prove comparison principles between viscosity semicontinuous sub- and supersolutions of the generalized Dirichlet problem (in the sense of viscosity solutions) for the Levi Monge-Ampère equation. As a consequence of this result and of the Perron's method we get the existence of a continuous solution of the Dirichlet problem related to the prescribed Levi curvature equation under suitable assumptions on the boundary data and on the Levi curvature of the domain. We also show that such a solution is Lipschitz continuous by building Lipschitz continuous barriers and by applying a weak Bernstein method.
2006
Existence and Uniqueness of Lipschitz Continuous Graphs with Prescribed Levi Curvature / F. Da Lio; A. Montanari. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 23:(2006), pp. 1-28. [10.1016/j.anihpc.2004.10.006]
F. Da Lio; A. Montanari
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/6070
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