TY - JOUR
T1 - A Generalised Monge-Ampère Equation
AU - Pingali , Vamsi P.
JO - Journal of Partial Differential Equations
VL - 4
SP - 333
EP - 346
PY - 2014
DA - 2014/12
SN - 27
DO - http://doi.org/10.4208/jpde.v27.n4.4
UR - https://global-sci.org/intro/article_detail/jpde/5146.html
KW - Monge-Ampère equations
KW - Hessian equations
KW - Evans-Krylov theory
AB -  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.