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arXiv · 2103.12502

Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets

Simon Bortz·John Hoffman·Steve Hofmann·José Luis Luna Garcia·Kaj Nyström
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Abstract

Let $E \subset \mathbb R^{n+1}$ be a parabolic uniformly rectifiable set. We prove that every bounded solution $u$ to $$\partial_tu- Δu=0, \quad \text{in} \quad \mathbb R^{n+1}\setminus E$$ satisfies a Carleson measure estimate condition. An important technical novelty of our work is that we develop a corona domain approximation scheme for $E$ in terms of regular Lip(1/2,1) graph domains. This approximation scheme has an analogous elliptic version which is an improvement of the known results in that setting.

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Simon Bortz, John Hoffman, Steve Hofmann, José Luis Luna Garcia, Kaj Nyström. 2021-03-23. Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets. https://doi.org/10.2140/apde.2023.16.1061

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