Asymptotic average solutions for second order hypoelliptic PDEs
Analysis of PDEs
2025-04-29 v1
Abstract
Following an analogous procedure with that used in \cite{kogoj_lanconelli_pizzetti}, in turn inspired by a 1909 paper by Pizzetti \cite{pizzetti}, we introduce the notion of {\it asymptotic average solutions} for hypoelliptic linear partial differential operators with non-negative characteristic form. This notion makes every Poisson equation with continuous data pointwise solvable.
Cite
@article{arxiv.2504.19240,
title = {Asymptotic average solutions for second order hypoelliptic PDEs},
author = {Alessia E. Kogoj},
journal= {arXiv preprint arXiv:2504.19240},
year = {2025}
}