Email this article Remark on the Hӧlder Continuity of p(x)-Harmonic Functions
- Authors: Alkhutov Y.A.1,2, Krasheninnikova O.V.1
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Affiliations:
- A. G. and N. G. Stoletov Vladimir State University
- Vladimir branch of the Financial University under the Government of the Russian Federation
- Issue: Vol 216, No 2 (2016)
- Pages: 147-154
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237774
- DOI: https://doi.org/10.1007/s10958-016-2893-z
- ID: 237774
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Abstract
We consider a p(x)-harmonic equation, where p(x) is measurable in Ω and is separated from 1 and infinity. It is shown that if p(x) is a radial function of x − x0, in a neighborhood of a point x0 ∈ Ω i.e., p(x) = p(|x − x0|) and p(t) is nonincreasing on (0, d), then p(x) is Hӧlder continuous at the point x0. Bibliography: 11 titles.
About the authors
Yu. A. Alkhutov
A. G. and N. G. Stoletov Vladimir State University; Vladimir branch of the Financial University under the Government of the Russian Federation
Author for correspondence.
Email: yurij-alkhutov@yandex.ru
Russian Federation, 87, Gor’kogo St., Vladimir, 600000; 1, Tikhonravova St., Vladimir, 600037
O. V. Krasheninnikova
A. G. and N. G. Stoletov Vladimir State University
Email: yurij-alkhutov@yandex.ru
Russian Federation, 87, Gor’kogo St., Vladimir, 600000
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