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Volume 27, Issue 4
A Generalised Monge-Ampère Equation

Vamsi P. Pingali

DOI: 10.4208/jpde.v27.n4.4

J. Part. Diff. Eq., 27 (2014), pp. 333-346.

Published online: 2014-12

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  • 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.
  • Keywords

Monge-Ampère equations Hessian equations Evans-Krylov theory

  • AMS Subject Headings

35J96, 53C07

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

vpingali@math.jhu.edu (Vamsi P. Pingali)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-27-333, author = {Pingali , Vamsi P.}, title = {A Generalised Monge-Ampère Equation}, journal = {Journal of Partial Differential Equations}, year = {2014}, volume = {27}, number = {4}, pages = {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.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n4.4}, url = {http://global-sci.org/intro/article_detail/jpde/5146.html} }
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.
Vamsi P. Pingali. (2019). A Generalised Monge-Ampère Equation. Journal of Partial Differential Equations. 27 (4). 333-346. doi:10.4208/jpde.v27.n4.4
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