We outline several results of Potential Theory for a class of linear par-tial differential operators L of the second order in divergence form. Under essentially the sole assumption of hypoellipticity, we present a non-invariant homogeneous Harnack inequality for L; under different geometrical assumptions on L (mainly, under global doubling/Poincaré assumptions), it is described how to obtainan invariant, non-homogeneous Harnack inequality. When L is equipped with a global fundamental solution Γ, further Potential Theory results are available (such as the Strong Maximum Principle). We present some assumptions on L ensuring that such a Γ exists.

Potential theory results for a class of PDOs admitting a global fundamental solution

A Bonfiglioli
2019

Abstract

We outline several results of Potential Theory for a class of linear par-tial differential operators L of the second order in divergence form. Under essentially the sole assumption of hypoellipticity, we present a non-invariant homogeneous Harnack inequality for L; under different geometrical assumptions on L (mainly, under global doubling/Poincaré assumptions), it is described how to obtainan invariant, non-homogeneous Harnack inequality. When L is equipped with a global fundamental solution Γ, further Potential Theory results are available (such as the Strong Maximum Principle). We present some assumptions on L ensuring that such a Γ exists.
2019
"Analysis and partial differential equations: perspectives from developing countries" in Springer Proc. Math. Stat.
65
83
A Bonfiglioli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/737488
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