Description

• Title:
  Existence results for fractional Brezis-Nirenberg type problems in unbounded domains
• Creator:
  Shen, Yansheng;
  Wang, Xumin
• Description:
  In this paper we study the fractional Brezis-Nirenberg type problems in unbounded cylinder-type domains \begin{align*} \begin{cases} (-\Delta)^{s}u-\mu\dfrac{u}{|x|^{2s}}=\lambda u+|u|^{2^{\ast}_{s}-2}u& \text{in } \Omega,\\ u=0 & \text{in } \mathbb{R}^{N}\setminus \Omega, \end{cases} \end{align*} where $(-\Delta)^{s}$ is the fractional Laplace operator with $s\in(0,1)$, $\mu\in[0,\Lambda_{N,s})$ with $\Lambda_{N,s}$ the best fractional Hardy constant, $\lambda> 0$, $N> 2s$ and $2^{\ast}_{s}={2N}/({N-2s})$ denotes the fractional critical Sobolev exponent. By applying the fractional Poincaré inequality together with the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove an existence result to the equation.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2022 Yansheng Shen, Xumin Wang;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2022.12.10
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 60, No 2 (December 2022); 517 - 546;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/41315/34033 ;https://apcz.umk.pl/TMNA/article/view/41315/34034
• Subject:
  Fractional Brezis-Nirenberg type problems;
  unbounded cylinder type domains;
  fractional Poincaré inequalities;
  concentration-compactness principle;
  Primary: 35A15, 35A23;
  Secondary: 35R11, 46E35
• Identifier: https://apcz.umk.pl/TMNA/article/view/41315
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other