系列学术活动之（16）

题    目：

Weighted global gradient estimates for elliptic   boundary value problems on non-smooth domains

摘    要：

Let $n\ge2$ and $\Omega\subset\mathbb{R}^n$ be a   bounded NTA domain. In this talk, we introduce (weighted) global gradient   estimates for Dirichlet/Neumann boundary value problems of second order   elliptic equations of divergence form with an elliptic symmetric part and a   BMO anti-symmetric part in $\Omega$. More precisely, for any given   $p\in(2,\infty)$, we show that a weak reverse H\older inequality with   exponent $p$ implies the global $W^{1,p}$ estimate and the global weighted   $W^{1,q}$ estimate, with $q\in[2,p]$ and some Muckenhoupt weights, of   solutions to Dirichlet boundary value problems. We further give some global   gradient estimates for solutions to Dirichlet/Neumann boundary value problems   of second order elliptic equations of divergence form with small   $\mathrm{BMO}$ symmetric part and small $\mathrm{BMO}$ anti-symmetric part,   respectively, on bounded Lipschitz domains, quasi-convex domains, Reifenberg   flat domains, $C^1$ domains, or (semi-)convex domains, in weighted Lebesgue   spaces. This talk is based on the joint work with Profs. Dachun Yang and Wen   Yuan.

报 告 人：

杨四辈，博士，兰州大学

时    间：

2021年10月22日19：00-21：00

地    点：

腾讯会议

 报告人简介：

杨四辈, 2013年毕业于北京师范大学, 获博士学位, 现为兰州大学数学与统计学院青年教授, 主要从事调和分析及其应用的研究. 与他人合作, 已在Trans. Amer. Math. Soc., J.   Differential Equations, Indiana Univ. Math. J., Rev. Mat. Iberoam., Commun.   Contemp. Math., J. Geom. Anal.等国内外重要刊物上发表学术论文40余篇. 主持完成国家自然科学基金青年项目1项，目前主持国家自然科学基金面上项目1项.