Effect of the Domain Geometry on the Solutions to Fractional Brezis-Nirenberg Problem. (18th July 2019)

• Record Type: Journal Article
• Authors: Tian, Qiaoyu; Xu, Yonglin
• Other Names: Latushkin Yuri Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2019(2019)
• Publication Date: 2019-07-18
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2019/1093804
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we consider the Brezis-Nirenberg problem for the nonlocal fractional elliptic equationA α u x = N N - 2 α u x p + ε u x, x ∈ Ω, u x > 0, x ∈ Ω, u ( x ) = 0, x ∈ ∂ Ω, where0 < α < 1 is fixed, p = N + 2 α / N - 2 α, ε is a small parameter, andΩ is a bounded smooth domain ofR N ( N ≥ 4 α ) .A α denotes the fractional Laplace operator defined through the spectral decomposition. Under some geometry hypothesis on the domainΩ, we show that all solutions to this problem are least energy solutions.