Scholarlink

<p>We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding Sobolev inequality, detecting the optimal constant, which we show that is never achieved. Moreover, we present an existence (and nonexistence) theory for the corresponding subcritical perturbation problem.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Brezis-Nirenberg type result for mixed local and nonlocal operators

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月21日

查看全文
  • Stefano Biagi,
  • Serena Dipierro,
  • Enrico Valdinoci,
  • Eugenio Vecchi

摘要

We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding Sobolev inequality, detecting the optimal constant, which we show that is never achieved. Moreover, we present an existence (and nonexistence) theory for the corresponding subcritical perturbation problem.