A nonlocal elliptic problem on a Heisenberg group
arXiv:2607.12758 · doi:10.1007/s12220-026-02510-0
summary
The paper investigates a nonlocal elliptic equation on the Heisenberg group with a source term given by a Radon measure, proving existence of weak solutions using a weak convergence method and introducing a new function space called the Walker space.
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.
Topics & keywords
#elliptic equations#nonlocal operators#Heisenberg group#measure data#weak solutions#function spacesRadon measureWalker spaceweak convergencenonlocal elliptic problemHeisenberg group