Sur les equations de Monge-Ampere. I

Lions, Pierre-Louis

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

Number

1-3

Publisher

Springer

Pages

1-43

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