Scholarlink

<p>In this paper, we introduce the second-order Sobolev spaces on Cayley graphs. We also prove the second-order Sobolev inequalities and the existence of extremal functions for best constants in supercritical cases. As an application, we derive positive ground state solutions for the <i>p</i>-biharmonic equations and the Lane-Emden systems on Cayley graphs of groups of polynomial growth.</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

Extremal functions for the second-order Sobolev inequality on Cayley graphs

  • 期刊论文

  • 发表日期：

    2025年7月8日

查看全文
  • Bobo Hua,
  • Ruowei Li,
  • Florentin Münch

摘要

In this paper, we introduce the second-order Sobolev spaces on Cayley graphs. We also prove the second-order Sobolev inequalities and the existence of extremal functions for best constants in supercritical cases. As an application, we derive positive ground state solutions for the p-biharmonic equations and the Lane-Emden systems on Cayley graphs of groups of polynomial growth.