Interior 𝐶² estimate for Monge-Ampère equation in dimension two
Jiakun Liu
Abstract
We obtain a genuine local <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C squared"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">C^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> estimate for the Monge-Ampère equation in dimension two, by using the partial Legendre transform.
Topics & Concepts
Dimension (graph theory)Legendre polynomialsLegendre transformationMathematicsMonge–Ampère equationMathematical analysisPure mathematicsGeometry and complex manifoldsGeometric Analysis and Curvature FlowsNonlinear Partial Differential Equations