Hardy inequalities for magnetic $p$-Laplacians

Cristian Cazacu; David Krejcirik; Nguyen Lam; Ari Laptev

Hardy inequalities for magnetic $p$-Laplacians

Analysis of PDEs 2025-02-05 v2 Mathematical Physics math.MP Spectral Theory

Authors: Cristian Cazacu , David Krejcirik , Nguyen Lam , Ari Laptev

Abstract

We establish improved Hardy inequalities for the magnetic $p$ -Laplacian due to adding nontrivial magnetic fields. We also prove that for Aharonov-Bohm magnetic fields the sharp constant in the Hardy inequality becomes strictly larger than in the case of a magnetic-free $p$ -Laplacian. We also post some remarks with open problems.

Keywords

hardy inequalities

Cite

@article{arxiv.2201.02482,
  title  = {Hardy inequalities for magnetic $p$-Laplacians},
  author = {Cristian Cazacu and David Krejcirik and Nguyen Lam and Ari Laptev},
  journal= {arXiv preprint arXiv:2201.02482},
  year   = {2025}
}