Potential Analysis

, Volume 24, Issue 3, pp 267–301 | Cite as

Regularity of Degenerate Monge–Ampère and Prescribed Gaussian Curvature Equations in Two Dimensions

  • Eric T. SawyerEmail author
  • Richard L. Wheeden


We use a priori inequalities for quasilinear equations to obtain a regularity theorem for the Dirichlet problem for the Monge–Ampère equation,
and the prescribed Gaussian curvature equation,
where k(x,y) is close to a function of one variable alone when k is small, but permitted to vanish to infinite order.


Monge–Ampère quasilinear regularity 


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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.McMaster UniversityHamilton
  2. 2.Rutgers UniversityNew Brunswick

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