A Generalised Monge-Ampère Equation

A Generalised Monge-Ampère Equation

Year:    2014

Author:    Vamsi P. Pingali

Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 4 : pp. 333–346

Abstract

We consider a generalised complex Monge-Ampère equation on a compact Kähler manifold and treat it using the method of continuity. For complex surfaces we prove an existence result. We also prove that (for three-folds and a related real PDE in a ball in R^3) as long as the Hessian is bounded below by a pre-determined constant (whilst moving along themethod of continuity path), a smooth solution exists. Finally, we prove existence for another real PDE in a 3-ball, which is a local real version of a conjecture of X. X. Chen.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v27.n4.4

Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 4 : pp. 333–346

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Monge-Ampère equations

Author Details

Vamsi P. Pingali

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