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Harmonic spaces associated with parabolic and elliptic differential operators. (English) Zbl 0664.31011

The aim of the article is to construct harmonic spaces (Bauer and Brelot spaces) which are associated with linear parabolic and elliptic differential operators of second order in nondivergence form under weak assumptions on the coefficients.
The results are formulated in terms of diffusion processes. They are obtained using probabilistic technics (martingale approach to diffusion processes, limit theorem etc.) and Krylov’s Harnack inequality for parabolic and elliptic equations.
Reviewer: P.Kröger

MSC:

31D05 Axiomatic potential theory
60J45 Probabilistic potential theory
31B35 Connections of harmonic functions with differential equations in higher dimensions
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References:

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