永利yl8886-№1

学术活动(2021-16) 杨四辈《Weighted global gradient estimates for elliptic boundary value problems on non-smooth domains》

发布者:王恒斌   发布时间:2021-10-22  浏览次数:10

系列学术活动之(16

   目:

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

 

    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

   间:

202110221900-2100

   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, 现为兰州大学永利yl8886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.


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