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