\(W^{1,p}_{\varphi}\)-estimates for Green's functions of the linearized Monge-Ampère operator

DOI10.1007/s00229-016-0874-7zbMath1384.35015OpenAlexW2492672184MaRDI QIDQ512827

Diego Maldonado

Publication date: 2 March 2017

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-016-0874-7

zbMATH Keywords

Green's functionlinearized Monge-Ampère operator

Mathematics Subject Classification ID

Green's functions for elliptic equations (35J08) Monge-Ampère equations (35J96)

Related Items (10)

On certain degenerate and singular elliptic PDEs. III: Nondivergence form operators and \(RH_\infty\)-weights ⋮ Harnack inequality for the fractional nonlocal linearized Monge-Ampère equation ⋮ On certain degenerate and singular elliptic PDEs I: nondivergence form operators with unbounded drifts and applications to subelliptic equations ⋮ On certain degenerate and singular elliptic PDEs. II: Divergence-form operators, Harnack inequalities, and applications ⋮ Fractional elliptic equations in nondivergence form: definition, applications and Harnack inequality ⋮ Morrey inequalities in the Monge-Ampère quasi-metric structure ⋮ Global Hölder estimates for 2D linearized Monge-Ampère equations with right-hand side in divergence form ⋮ Poincaré and Sobolev inequalities in the Monge-Ampère quasi-metric structure ⋮ Linear parabolic operators of Monge-Ampère. I: Nondivergence-form degenerate/singular PDEs ⋮ On convex functions and elliptic operators

Cites Work

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• On the \(W^{2,1+\varepsilon }\)-estimates for the Monge-Ampère equation and related real analysis
• Harnack's inequality for solutions to the linearized Monge-Ampère operator with lower-order terms
• The Monge-Ampère quasi-metric structure admits a Sobolev inequality
• \(W^{4, p}\) solution to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations
• Remarks on the Green's function of the linearized Monge-Ampère operator
• The Monge–Ampère equation and its link to optimal transportation
• Properties of the solutions of the linearized Monge-Ampere equation
• Heat Kernels and Green Functions on Metric Measure Spaces
• The Monge-Ampère equation

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