一、报告题目：Extrapolation and weighted estimates in Homogenization of Systems of Elasticity

二、报告人：耿俊 教授

三、时 间：2022 年 3 月 26 日 (周六)上午 9:50--10:30.

四、腾讯会议号：762-7964-8189

报告摘要： For a fixed bounded Lipschitz domain and a family of systems of linear elasticity with rapidly oscillating periodic coefficients, we investigate a necessary and sufficient condition that an $A_1$ weight $\omega$ must satisfy in order for the weighted $W^{1,2}(\omega)$ estimates for weak solutions of Neumann problems to be true. Moreover, in any Lipschitz domain, we prove that the uniform $W^{1,p}$ estimates for solutions to the Neumann problem hold for $\frac{2d}{d+1}-\delta<p<\frac{2d}{d-1}+\delta$. The ranges are sharp for $d=2, 3$. Finally, we prove an extrapolation result for $L^p$ Dirichlet problems for systems of linear elasticity.

报告人简介：耿俊，2011年获美国肯塔基大学博士学位，青年长江学者，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SIAM J. Math. Anal.、 Arch. Ration. Mech. Anal.、Anal. PDE、J. Differential Equations、Proc. Amer. Math. Soc.、J. Funct. Anal.、Indiana Univ. Math. J.、Adv. Math..等国内外重要期刊发表多项高质量研究成果。  

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