A free boundary problem for the parabolic Poisson kernel
| Autor: | Max Engelstein |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Chord (geometry)
Logarithm General Mathematics 010102 general mathematics Mathematical analysis Poisson kernel Mathematics::Analysis of PDEs 16. Peace & justice 01 natural sciences Parabolic partial differential equation Carleson measure symbols.namesake Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics Parabolic problem symbols Free boundary problem 010307 mathematical physics 0101 mathematics Analysis of PDEs (math.AP) 35R35 Mathematics |
| Zdroj: | Advances in Mathematics. 314:835-947 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2017.04.032 |
| Popis: | We study parabolic chord arc domains, introduced by Hofmann, Lewis and Nystr\"om, and prove a free boundary regularity result below the continuous threshold. More precisely, we show that a Reifenberg flat, parabolic chord arc domain whose Poisson kernel has logarithm in VMO must in fact be a vanishing chord arc domain (i.e. satisfies a vanishing Carleson measure condition). This generalizes, to the parabolic setting, a result of Kenig and Toro and answers in the affirmative a question left open in the aforementioned paper of Hofmann et al. A key step in this proof is a classification of "flat" blowups for the parabolic problem. Comment: 91 pages. Comments welcome |
| Databáze: | OpenAIRE |
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