English

Asymptotic average solutions to linear second order semi-elliptic PDEs: a Pizzetti-type Theorem

Analysis of PDEs 2022-09-20 v1

Abstract

By exploiting an old idea first used by Pizzetti for the classical Laplacian, we introduce a notion of {\it asymptotic average solutions} making pointwise solvable every Poisson equation Lu(x)=f(x)\mathcal{L} u(x)=-f(x) with continuous data ff, where L\mathcal{L} is a hypoelliptic linear partial differential operator with positive semidefinite characteristic form.

Keywords

Cite

@article{arxiv.2209.08394,
  title  = {Asymptotic average solutions to linear second order semi-elliptic PDEs: a Pizzetti-type Theorem},
  author = {Alessia E. Kogoj and Ermanno Lanconelli},
  journal= {arXiv preprint arXiv:2209.08394},
  year   = {2022}
}
R2 v1 2026-06-28T01:30:35.293Z