New Approach for Interior Regularity of Monge-Amp\`{e}re Equations
Ruosi Chen, Xingchen Zhou
TL;DR
This paper introduces a novel integral method to analyze the interior regularity of strictly convex solutions to the Monge-Ampère equation, advancing understanding of solution smoothness.
Contribution
The paper develops a new integral approach specifically for establishing interior regularity of solutions to the Monge-Ampère equation.
Findings
Established interior regularity results using the new integral method.
Provided a framework that could be applicable to other fully nonlinear PDEs.
Enhanced theoretical understanding of convex solutions to Monge-Ampère equations.
Abstract
By developing an integral approach, we present a new method for the interior regularity of strictly convex solution of the Monge-Amp\`{e}re equation .
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations