TY - JOUR
AU - Lanconelli, Ermanno
AB - By exploiting an old idea first used by Pizzetti for the classical Laplacian, we introduce a notion of asymptotic average solutions making pointwise solvable every Poisson equation ℒu(x)=−f(x)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}${\mathcal {L}} u(x)=-f(x)$\end{document} with continuous data f, where ℒ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}${\mathcal {L}}$\end{document} is a hypoelliptic linear partial differential operator with positive semidefinite characteristic form.
TI - Asymptotic Average Solutions to Linear Second Order Semi-Elliptic PDEs: A Pizzetti-Type Theorem
JF - Potential Analysis
DO - 10.1007/s11118-023-10063-y
DA - 2024-02-01
UR - https://www.deepdyve.com/lp/springer-journals/asymptotic-average-solutions-to-linear-second-order-semi-elliptic-pdes-mA0J940Qmb
SP - 615
EP - 626
VL - 60
IS - 2
DP - DeepDyve
ER -