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On the fine properties of parabolic measures associated to strongly degenerate parabolic operators of Kolmogorov type. (English) Zbl 1470.35208

In this paper the authors are concerned with the fine properties of parabolic measures, defined with respect to an appropriate unbounded Lipschitz domain \(\Omega\) associated to suitable strongly degenerate parabolic operators. The authors prove that the associated parabolic measure is absolutely continuous with respect to a surface measure and that the associated Radon-Nikodym derivative defines an \(A_\infty\)-weight with respect to the surface measure.

MSC:

35K65 Degenerate parabolic equations
35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
35B65 Smoothness and regularity of solutions to PDEs
35H20 Subelliptic equations
35R03 PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.
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References:

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