报告人：杨四辈教授（兰州大学）
报告时间：2021年4月12日周一下午3：00-4：00
报告地点：腾讯会议ID：543 8265 5387
报告题目：Global gradient estimates for Dirichlet problems of elliptic operators
with a BMO anti-symmetric part on non-smooth domains
报告摘要： 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 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. 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 $\mathrm{BMO}$ 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. 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.