Asymptotic average solutions to linear second order semi-elliptic PDEs: a Pizzetti-type Theorem
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 L u(x)=-f(x) with continuous data f, where L is a hypoelliptic linear partial differential operator with positive semidefinite characteristic form.
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