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Aleksandrov-Bakelman-Pucci maximum principle for Ln-viscosity solutions of uniformly elliptic equations with unbounded terms: The critical case
Abstract
We prove the Aleksandrov-Bakelman-Pucci maximum principle for Ln-viscosity sub/super-solutions of fully nonlinear uniformly elliptic equations in Ω⊂ℝn with the drift coefficient γ such that γ(ln(1+γ))(n−1)/n∈ Ln(Ω). The approach is based on convex duality and Trudinger-Moser type inequalities.
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BibTeX
@misc{swiech2026aleksandrovbakelmanpucci,
title = {{Aleksandrov-Bakelman-Pucci maximum principle for $L^n$-viscosity solutions of uniformly elliptic equations with unbounded terms: The critical case}},
author = {Andrzej Święch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03918},
eprint = {2610.03918},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03918},
}
RIS
TY - UNPB
TI - Aleksandrov-Bakelman-Pucci maximum principle for L^n-viscosity solutions of uniformly elliptic equations with unbounded terms: The critical case
AU - Andrzej Święch
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03918
UR - https://arxiv.org/abs/2610.03918
AB - We prove the Aleksandrov-Bakelman-Pucci maximum principle for L^n-viscosity sub/super-solutions of fully nonlinear uniformly elliptic equations in Ω⊂ℝ^n with the drift coefficient γ such that γ(ln(1+γ))^(n−1)/n∈ L^n(Ω). The approach is based on convex duality and Trudinger-Moser type inequalities.
ER -