best365网页版登录学术报告
--- 分析、偏微分方程与动力系统讨论班(2024春季第11讲)
The Neumann Problem for the Stokes System on Convex Domains
耿俊(兰州大学)
时间:2024年05月27日(周一)上午09:30-10:30
地点:#腾讯会议:509-766-8696 会议密码:654321
点击链接直接加入会议:
https://meeting.tencent.com/p/5097668696
摘要: We show that the Neumann problem for Stokes system on convex domain $\Omega$ with boundary data in $L^p(\partial\Omega)$ is uniquely solvable for
\begin{equation*}
\left\{
\aligned
& 1<p<\infty \qquad\qquad\qquad\qquad\quad~~\mbox{ if } d=2, \\
& 1<p<4+\e \qquad\qquad\qquad\qquad ~~\mbox{ if } d=3, \\
& \frac{2(d-1)}{d+1}-\e<p<\frac{2(d-1)}{d-2}+\e ~~\mbox{ if } d\geq 4
\endaligned
\right.
\end{equation*}
and the $W^{1,p}$ estimate for the Poisson problem is true for
\begin{equation*}
\left\{
\aligned
& 1<p<\infty \qquad\qquad\qquad\qquad\quad~~\mbox{ if } d=2, \\
& \frac{2d}{d+2}-\e<p<\frac{2d}{d-2}+\e. ~~~~~~~~\mbox{ if } d\geq 3
\endaligned
\right.
\end{equation*}
The ranges of $p$ are sharp for $d=2$ and these intervals are larger than
the known interval on Lipschitz domain.
报告人简介: 耿俊,2011年获美国肯塔基大学博士学位,国家级高层次青年人才,现任兰州大学教授、博士生导师。主要从事非光滑区域上的椭圆边值问题和均匀化理论的研究。先后主持国家自然科学基金青年基金1项、 面上项目2项。在Adv. Math.、Arch. Ration. Mech. Anal.、Anal. PDE、J. Funct. Anal.、SIAM J. Math. Anal.、J. Differential Equations、Proc. Amer. Math. Soc.、Indiana Univ. Math. J.等国内外重要期刊发表多项高质量研究成果。
欢迎大家参加!