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Sur les equations de Monge-Ampere. I

Lions, Pierre-Louis (1983), Sur les equations de Monge-Ampere. I, Manuscripta Mathematica, 41, 1-3, p. 1-43. http://dx.doi.org/10.1007/BF01165928

Type
Article accepté pour publication ou publié
Date
1983
Journal name
Manuscripta Mathematica
Volume
41
Number
1-3
Publisher
Springer
Pages
1-43
Publication identifier
Metadata
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Author(s)
Lions, Pierre-Louis
Abstract (EN)
In this paper we study the real Monge-Ampère equations: det(D2u)= f(x) in 0, u convex in 0, u=0 on ∂0, and we introduce a new method for solving these equations which enables us to show the existence of regular solutions. This method uses only p.d.e. techniques and does not use any geometrical results. Furthermore, it enables us to solve quasilinear Monge-Ampère equations.
Subjects / Keywords
Monge-Ampère equations