PreprintCC BY 4.0arXiv
On an evolutionary equation involving the nonlocal infinity Laplacian
Abstract
We study the evolutionary equation (∂ u)/(∂ t) = (ℒ∞)αu in Ω, where (ℒ∞)αu denotes a nonlocal infinity Laplacian acting on the function u, 0<α≤ 1 and Ω is a bounded open set in ℝn+1. We prove existence and uniqueness using Perron's method for the Dirichlet problem when Ω is a cylinder and 0<α<1.
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BibTeX
@misc{fejne2026evolutionary,
title = {{On an evolutionary equation involving the nonlocal infinity Laplacian}},
author = {Frida Fejne},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11311},
eprint = {2609.11311},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11311},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On an evolutionary equation involving the nonlocal infinity Laplacian
AU - Frida Fejne
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11311
UR - https://arxiv.org/abs/2609.11311
AB - We study the evolutionary equation (∂ u)/(∂ t) = (ℒ_∞)^αu in Ω, where (ℒ_∞)^αu denotes a nonlocal infinity Laplacian acting on the function u, 0<α≤ 1 and Ω is a bounded open set in ℝ^n+1. We prove existence and uniqueness using Perron's method for the Dirichlet problem when Ω is a cylinder and 0<α<1.
ER -