Some multi-valued solutions to Monge-Ampere equations
Luis Caffarelli, YanYan Li
TL;DR
This paper constructs various multi-valued solutions to the Monge-Ampere equation in higher dimensions, expanding the understanding of solutions to this complex nonlinear PDE.
Contribution
It introduces new types of multi-valued solutions to the Monge-Ampere equation in higher dimensions, which were not previously known.
Findings
Multiple types of multi-valued solutions constructed
Extension of solutions to higher-dimensional cases
Advancement in understanding Monge-Ampere equations
Abstract
We construct several types of multi-valued solutions to the Monge-Ampere equation in higher dimensions.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations