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Nonlinear parabolic thin sets and parabolic Wolff inequalities
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Nonlinear parabolic thin sets and parabolic Wolff inequalities
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Paper
Nonlinear parabolic thin sets and parabolic Wolff inequalities
2026
Overview
We prove a parabolic analogue of Wolff's inequality adapted to the intrinsic scaling \\(_c(x,t)=(cx,c^2t)\\) and formulated in terms of time-backward parabolic dyadic rectangles. As a consequence, we obtain equivalent characterizations of parabolic \\(( q)\\)-thinness in this geometric setting and establish the associated Kellogg and Choquet properties. We further use the notion of \\(( 2)\\)-thinness defined in terms of fractional heat balls and prove that the sets of irregular boundary points \\(z_0ın\\) for the heat operator \\(_t-\\) and for the degenerate operator \\(La=_t(|y|^a)-div(|y|^a)\\) in \\(^d+1\\) are negligible with respect to the thermal capacity \\(cap^ T\\) and the parabolic Bessel capacity \\(C_ 2\\), respectively.
Publisher
Cornell University Library, arXiv.org
Subject
