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arXiv · 2504.19240

Asymptotic average solutions for second order hypoelliptic PDEs

Alessia E. Kogoj
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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 $\elle u(x)=-f(x)$ with continuous data $f$ pointwise solvable.

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Alessia E. Kogoj. 2025-04-27. Asymptotic average solutions for second order hypoelliptic PDEs. https://arxiv.org/abs/2504.19240

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