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) with continuous data f, where L is a hypoelliptic linear partial differential operator with positive semidefinite characteristic form.
Asymptotic Average Solutions to Linear Second Order Semi-Elliptic PDEs: A Pizzetti-Type Theorem
Kogoj, Alessia E.
;
2023
Abstract
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) with continuous data f, where L is a hypoelliptic linear partial differential operator with positive semidefinite characteristic form.File in questo prodotto:
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