English

A nonlocal elliptic problem on a Heisenberg group

Analysis of PDEs 2026-07-14 v1
Authors: Debajyoti Choudhuri , Lamine Mbarki , Olimpio Hiroshi Miyagaki
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Abstract

We study an elliptic nonlocal problem driven by a source term which is a Radon measure. We prove the existence of a weak solution by a weak convergence method. In the process, we define a new function space which we name the Walker space. The question about the existence of infinitely many nontrivial solutions leads to an interesting conjecture.

Keywords

nonlocal elliptic problem Heisenberg group Radon measure weak solution Walker space

Cite

@article{arxiv.2607.12758,
  title  = {A nonlocal elliptic problem on a Heisenberg group},
  author = {Debajyoti Choudhuri and Lamine Mbarki and Olimpio Hiroshi Miyagaki},
  journal= {arXiv preprint arXiv:2607.12758},
  year   = {2026}
}