Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets

Abstract

Let E ⊂ R n+1 be a parabolic uniformly rectifiable set.We prove that every bounded solution u tosatisfies 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.Contents 1. Introduction 1 2. Preliminaries 4 3. Domain approximation in stopping time regimes 9 4. Carleson Measure Estimates: Proof of Theorems 1.1 and 1.3 18 5.Further remarks 21 Appendix A. Proof of Lemma 3.24 23 References 27

Locations

• Analysis & PDE - View - PDF
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