Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
Francesca Da Lio, Annamaria Montanari (2006)
Annales de l'I.H.P. Analyse non linéaire
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Displaying similar documents to “On the smoothness of viscosity solutions of the prescribed Levi-curvature equation”
Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
regularity of solutions of a quasilinear equation related to the Levi operator
G. Citti (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Smooth regularity for solutions of the Levi Monge-Ampère equation
Francesca Lascialfari, Annamaria Montanari (2001)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We present a smooth regularity result for strictly Levi convex solutions to the Levi Monge-Ampère equation. It is a fully nonlinear PDE which is degenerate elliptic. Hence elliptic techniques fail in this situation and we build a new theory in order to treat this new topic. Our technique is inspired to those introduced in [3] and [8] for the study of degenerate elliptic quasilinear PDE’s related to the Levi mean curvature equation. When the right hand side has the meaning of total curvature...
Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity and with natural growth
Sofia Giuffrè, Giovanna Idone (2005)
Bollettino dell'Unione Matematica Italiana
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In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second order discontinuous elliptic systems with nonlinearity and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets are always...
Comparison principles and pointwise estimates for viscosity solutions of nonlinear elliptic equations.
Neil S. Trudinger (1988)
Revista Matemática Iberoamericana
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We prove comparison principles for viscosity solutions of nonlinear second order, uniformly elliptic equations, which extend previous results of P. L. Lions, R. Jensen and H. Ishii. Some basic pointwise estimates for classical solutions are also extended to continuous viscosity solutions.