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On the Aleksandrov--Bakelman--Pucci estimates for the weighted $1$-Laplacian
Abstract
We establish Aleksandrov--Bakelman--Pucci-type estimates for viscosity subsolutions of Poisson equations associated with the weighted $1$-Laplacian and, more generally, with fully nonlinear operators acting on the Hessian in directions orthogonal to the gradient. A key feature of the proof is that the quasiconcave envelope plays the role of the concave envelope in the classical ABP estimate.
Related
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BibTeX
@misc{kitano2026aleksandrovbakelmanpucci,
title = {{On the Aleksandrov--Bakelman--Pucci estimates for the weighted $1$-Laplacian}},
author = {Shuhei Kitano},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00719},
eprint = {2609.00719},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00719},
}
RIS
TY - UNPB
TI - On the Aleksandrov--Bakelman--Pucci estimates for the weighted $1$-Laplacian
AU - Shuhei Kitano
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00719
UR - https://arxiv.org/abs/2609.00719
AB - We establish Aleksandrov--Bakelman--Pucci-type estimates for viscosity subsolutions of Poisson equations associated with the weighted $1$-Laplacian and, more generally, with fully nonlinear operators acting on the Hessian in directions orthogonal to the gradient. A key feature of the proof is that the quasiconcave envelope plays the role of the concave envelope in the classical ABP estimate.
ER -