Year: 2024
Type: article
Abstract: This work is devoted to Lipschitz conditions on bounded harmonic functions on the upper half-space in Rn. Among other results, we prove the following one. Let U(x′,xn) be a real-valued bounded harmonic function on the upper half-space R+n={(x′,xn):x′∈Rn−1,xn∈(0,∞)}, which is continuous on the closure of this domain. Assume that for α∈(0,1), there exists a constant C such that for every x′∈Rn−1, we have ||U|(x′,xn)−|U|(x′,0)|≤Cxnα, xn∈(0,∞). Then there exists a constant C˜ such that |U(x)−U(y)|≤C˜|x−y|α,x,y∈R+n.
Source: Illinois Journal of Mathematics
Author: Marijan Marković
Institution: University of Montenegro
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406775323