Description

• Title:
  Ground state solutions for a critical fractional Laplacian equation in unbounded domains: existence and regularity
• Creator:
  Shen, Yansheng
• Description:
  In this work we study the following fractional critical problem \begin{align*} \begin{cases} (-\Delta)^{s}u=\lambda|u|^{q-2}u+|u|^{2_{s}^{\ast}-2}u& \mbox{in } \Omega, \\ u=0 & \text{in }\mathbb{R}^{N}\setminus \Omega, \end{cases} \end{align*} where $\Omega$ is an open unbounded strip-like domain in $\mathbb{R}^{N}$, $N> 2s$ with $s\in(0,1)$, $\lambda> 0$, $q\in[2,2_{s}^{\ast})$ and $2_{s}^{\ast}=2N/(N-2s)$. By variational methods, we prove the existence of positive ground state solutions to the problem. Further, we study the regularity of these solutions. Precisely, using a Brézis-Kato type estimate for unbounded domains, we establish the $L^{\infty}$-bound on nonnegative solutions of the equation for certain range of $q$. The present work extends the existence and regularity results for fractional Laplace equations to unbounded domains.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2024 Yansheng Shen
• Date:
  2024.12.28
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 2 (December 2024); 621 - 653;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/57372/40914 ;https://apcz.umk.pl/TMNA/article/view/57372/40915
• Subject:
  Fractional Laplacian;
  ground state solutions;
  critical exponents;
  variational techniques;
  unbounded strip-like domains};
  35A15, 35S15, 46E35, 47G20
• Identifier: https://apcz.umk.pl/TMNA/article/view/57372
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other