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Energy Functionals and Complex Monge–Ampère Equations

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  10 February 2010

Zuoliang Hou  and
Qi Li
Zuoliang Hou
Affiliation:
Mathematics Department, Columbia University, 2990 Broadway, New York, NY 10027, USA (hou@math.columbia.edu; liqi@math.columbia.edu)
Qi Li
Affiliation:
Mathematics Department, Columbia University, 2990 Broadway, New York, NY 10027, USA (hou@math.columbia.edu; liqi@math.columbia.edu)
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Abstract

We introduce certain energy functionals to complex Monge–Ampère equations over bounded domains with inhomogeneous boundary conditions, and use these functionals to show the convergence of solutions to certain parabolic Monge–Ampère equations.

Keywords

energy functionalparabolic partial differential equationcomplex Monge–Ampère equation

MSC classification

Secondary: 35K60: Nonlinear initial value problems for linear parabolic equations 35K20: Initial-boundary value problems for second-order parabolic equations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 3 , July 2010 , pp. 463 - 476
Copyright
Copyright © Cambridge University Press 2010

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