Extremal functions for the second-order Sobolev inequality on groups of polynomial growth

Bobo Hua; Ruowei Li; Florentin Münch

Extremal functions for the second-order Sobolev inequality on groups of polynomial growth

Analysis of PDEs 2022-05-03 v1

Authors: Bobo Hua , Ruowei Li , Florentin Münch

Abstract

In this paper, we prove the second-order Sobolev inequalities on Cayley graphs of groups of polynomial growth. We use the discrete Concentration-Compactness principle to prove the existence of extremal functions for best constants in supercritical cases. As applications, we get the existence of positive ground state solutions to the $p$ -biharmonic equations and the Lane-Emden systems.

Keywords

sobolev inequality polynomial growth groups cayley graphs extremal functions concentration-compactness p-biharmonic equations lane-emden systems

Cite

@article{arxiv.2205.00150,
  title  = {Extremal functions for the second-order Sobolev inequality on groups of polynomial growth},
  author = {Bobo Hua and Ruowei Li and Florentin Münch},
  journal= {arXiv preprint arXiv:2205.00150},
  year   = {2022}
}

Comments

25 pages, 1 figure. arXiv admin note: text overlap with arXiv:2106.15982

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