Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces

Siegfried Carl; Kanishka Perera; Hossein Tehrani

Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces

Analysis of PDEs 2025-07-15 v1

Authors: Siegfried Carl , Kanishka Perera , Hossein Tehrani

Abstract

We prove new multiplicity results for some nonlocal critical growth elliptic equations in homogeneous fractional Sobolev spaces. The proofs are based on an abstract critical point theorem based on the ${\mathbb Z}_2$ -cohomological index and on a novel regularity result for fractional $p$ -Laplacian equations as well as on some compact embeddings.

Keywords

nonlocal equations fractional Laplacian Sobolev spaces critical growth mountain pass theorem

Cite

@article{arxiv.2507.09853,
  title  = {Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces},
  author = {Siegfried Carl and Kanishka Perera and Hossein Tehrani},
  journal= {arXiv preprint arXiv:2507.09853},
  year   = {2025}
}

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