$L_p$ 二进鞅与椭圆方程解的有界变差逼近
经典分析与常微分方程
2016-06-23 v3 偏微分方程分析
泛函分析
摘要
我们证明了从由 Carleson 泛函定义的局部有界变差函数空间到 的迹映射的连续性和满射性。扩展映射是通过停时论证构造的。这扩展了 Varopoulos 在 BMO 情形下与 Corona 定理相关的早期工作。我们还证明了椭圆非光滑散度型方程解的 Carleson 可逼近性结果，推广了 Hofmann、Kenig、Mayboroda 和 Pipher 在 情形下的结果。
引用
@article{arxiv.1405.2153,
title = {Bounded variation approximation of L_p dyadic martingales and solutions to elliptic equations},
author = {Tuomas Hytönen and Andreas Rosén},
journal= {arXiv preprint arXiv:1405.2153},
year = {2016}
}
备注
This is an extended version of an earlier arXiv preprint (not to be published) "Approximate and exact extensions of Lebesgue boundary functions", which also includes Lp epsilon-approximability results for divergence form elliptic equations. To this third version we have also added a section on applications to estimates of harmonic measure