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

Shuhei Kitano

math.AParXiv:2609.00719

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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