Harmonic spaces associated with parabolic and elliptic differential operators
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.
linear parabolic and elliptic differential operators
scientific article; zbMATH DE number 4086027
scientific article