Aleksandrov-Bakelman-Pucci maximum principle for $L^n$-viscosity solutions of uniformly elliptic equations with unbounded terms: The critical case
Year: 2026
Type: preprint
Abstract: We prove the Aleksandrov-Bakelman-Pucci maximum principle for $L^n$-viscosity sub/super-solutions of fully nonlinear uniformly elliptic equations in $Ω\subset\mathbb R^n$ with the drift coefficient $γ$ such that $γ(\ln(1+γ))^{\frac{n-1}{n}}\in L^n(Ω)$. The approach is based on convex duality and Trudinger-Moser type inequalities.
Source: arXiv (Cornell University)
Author: Święch, Andrzej
Institution: Georgia Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220651596