PreprintCC BY-NC-ND 4.0arXiv
On a higher-integrability estimate for Laplacians of convex solutions to the Monge-Ampère equation
Abstract
A maximum principle for certain strictly convex functions belonging to W2,1loc(Ω)∩ C1(Ω) is established and then applied to obtain a W2,1 +epsloc(Ω)-estimate.
Related
- Isolated singularities of solutions to the Yamabe equation in higher dimensions I
- Vanishing orders of Dirichlet solutions to the Schrödinger equation in dimensions three and higher
- Isolated singularities of solutions to the Yamabe equation in higher dimensions II
- Sharp Higher Integrability Theory, Part I: The Lp-norm of the Beurling--Ahlfors transform
- Higher Integrability, Generalized Symmetries, and Partially Topological Field Theories
BibTeX
@misc{maldonado2026higherintegrability,
title = {{On a higher-integrability estimate for Laplacians of convex solutions to the Monge-Ampère equation}},
author = {Diego Maldonado},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20216},
eprint = {2609.20216},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20216},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On a higher-integrability estimate for Laplacians of convex solutions to the Monge-Ampère equation
AU - Diego Maldonado
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20216
UR - https://arxiv.org/abs/2609.20216
AB - A maximum principle for certain strictly convex functions belonging to W^2,1_loc(Ω)∩ C^1(Ω) is established and then applied to obtain a W^2,1 +eps_loc(Ω)-estimate.
ER -