Speaker：Sibei Yang (Lanzhou University)

Time：2021-01-11 15:00

Location：Tencent Meeting ID：770 833 959（No Password）

Abstract:

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.