On a Higher-Integrability Estimate for Laplacians of Convex Solutions to the Monge-Ampère Equation

A maximum principle for certain strictly convex functions belonging to \(W_{\mathrm{loc}}^{2,1}(\Omega)\cap C^1(\Omega)\) is established and then applied to obtain a \(W_{\mathrm{loc}}^{2,1+\varepsilon}(\Omega)\)-estimate.

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Publication Details

Journal
Analysis in Theory and Applications
Published
2026-10-30
DOI
https://doi.org/10.4208/ata.oa-2026-0054
Primary Topic
Nonlinear Partial Differential Equations
Type
article
Field-Weighted Citation Impact
0.00

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article

On a Higher-Integrability Estimate for Laplacians of Convex Solutions to the Monge-Ampère Equation

Diego Maldonado
2 links
Analysis in Theory and Applications
Nonlinear Partial Differential Equations
article

On a Higher-Integrability Estimate for Laplacians of Convex Solutions to the Monge-Ampère Equation

Diego Maldonado
article en

Abstract

A maximum principle for certain strictly convex functions belonging to \(W_{\mathrm{loc}}^{2,1}(\Omega)\cap C^1(\Omega)\) is established and then applied to obtain a \(W_{\mathrm{loc}}^{2,1+\varepsilon}(\Omega)\)-estimate.

Analysis in Theory and Applications
Kansas State University (US)
Simons Foundation
Openalex Percentile: Top 34%
Nonlinear Partial Differential Equations
DOIOpen Access PDFOpenAlex
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On a Higher-Integrability Estimate for Laplacians of Convex Solutions to the Monge-Ampère Equation — Diego Maldonado · Analysis in Theory and Applications (2026) | TGRS Research Map | TGRS