Asymptotic average solutions for second order hypoelliptic PDEs
Abstract
Following an analogous procedure with that used in kogojlanconellipizzetti, in turn inspired by a 1909 paper by Pizzetti pizzetti, we introduce the notion of asymptotic average solutions for hypoelliptic linear partial differential operators with non-negative characteristic form. This notion makes every Poisson equation u(x)=-f(x) with continuous data f pointwise solvable.
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