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

：杨四辈教授
：2021-01-11 15:00
：腾讯会议APP（线上）

报告人：杨四辈（兰州大学）

时  间：1月11日15:00

地  点：腾讯会议ID：770 833 959（无设置密码）

内容摘要:

Let n ≥ 2 and Ω ⊂ Rn be a bounded NTA domain. In this talk, we introduce (weighted) global gradient estimates for Dirichlet boundary value problems of second order elliptic equations of divergence form with an elliptic symmetric part and a BMO antisymmetric part in Ω. More precisely, for any given p ∈ (2; ∞), we show that a weak reverse Holder inequality with exponent p implies the global W1,p estimate and the global weighted W1,p estimate, with q ∈[2; p] and some Muckenhoupt weights, of solutions to Dirichlet boundary value problems. As applications, we give some global gradient estimates for solutions to Dirichlet boundary value problems of second order elliptic equations of divergence form with small BMO symmetric part and small BMO anti-symmetric part, respectively, on bounded Lipschitz domains, quasi-convex domains, Reifenberg flat domains, C1 domains, or (semi-)convex domains, in weighted Lebesgue spaces. Furthermore, as further applications, we obtain the global gradient estimate, respectively, in (weighted) Lorentz spaces, (Lorentz–)Morrey spaces, (Musielak–)Orlicz spaces, and variable Lebesgue spaces. This talk is based on the joint work with Profs. Dachun Yang and Wen Yuan.

个人简介：

杨四辈, 现为兰州大学青年教授, 2013年6月于北京师范大学获博士学位(导师: 杨大春教授)。研究方向为调和分析及其在PDE中的应用. 与他人合作, 在Trans. Amer. Math. Soc., J. Differential Equations, Indiana Univ. Math. J., Rev. Mat. Iberoam., Commun. Contemp. Math., J. Geom. Anal., Sci. China Math.等国内外重要刊物上发表论文40 余篇. 目前主持国家自然科学基金面上项目一项, 主持完成国家自然科学基金青年基金一项。

 

联系人：杨东勇