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arXiv · 2609.00719

On the Aleksandrov--Bakelman--Pucci estimates for the weighted $1$-Laplacian

Shuhei Kitano
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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.

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Shuhei Kitano. 2026-09-01. On the Aleksandrov--Bakelman--Pucci estimates for the weighted $1$-Laplacian. https://arxiv.org/abs/2609.00719

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