Energy Functionals for the Parabolic Monge-Ampere Equation
Zuoliang Hou, Qi Li
TL;DR
This paper introduces energy functionals for the complex Monge-Ampere equation with inhomogeneous boundary conditions and demonstrates their use in proving the convergence of solutions to the parabolic Monge-Ampere equation.
Contribution
It presents new energy functionals tailored for the complex Monge-Ampere equation and applies them to establish convergence results for the parabolic version.
Findings
Energy functionals successfully used to analyze convergence
Convergence of solutions to the parabolic Monge-Ampere equation proven
Applicable to bounded domains with inhomogeneous boundary conditions
Abstract
We introduce certain energy functionals to the complex Monge-Ampere equation over a bounded domain with inhomogeneous boundary condition, and use these functionals to show the convergence of the solution to the parabolic Monge-Ampere equation.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Waves and Solitons