Fatou theorems for parabolic equations

Sweezy, Caroline

doi:10.1090/S0002-9939-96-03687-8

Fatou theorems for parabolic equations
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Proc. Amer. Math. Soc. 124 (1996), 2343-2355 Request permission

Abstract:

For elliptic parabolic operators with time dependent coefficients, bounded and measurable, the absolute continuity of the two caloric measures plus a Fatou theorem are shown to hold on the parabolic boundary of a smooth cylinder given a Carleson-type condition on the coefficients of the operators, and assuming one of the measures is a center doubling measure. Given a stronger Carleson condition, and no doubling assumption, another kind of Fatou theorem result holds. The method of proof follows that of Fefferman, Kenig and Pipher.

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