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, Volume 41, Issue 1–3, pp 1–43 | Cite as

Sur les equations de Monge-Ampere. I

  • Pierre-Louis Lions
Article

Abstract

In this paper we study the real Monge-Arapère 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.

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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Pierre-Louis Lions
    • 1
  1. 1.Ceremade Université Paris IX-DauphineParis Cedex 16

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