中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Nguyen Cong Phuc (Louisiana State University)
题 目：Comparison estimates and pointwise regularity for p-Laplace equations with measure data
时 间：2022.08.17（星期三）09:00-10:00
地 点：Zoom ID: 924 888 5804 Passcode: AMSS2022
Join Zoom Meeting :
https://us06web.zoom.us/j/9248885804?pwd=OXg2VDhBT0pxRkd1Z3RJS0NFMnRDdz09
摘 要：We present comparison estimates for $p$-Laplace type equations with measure data with emphasis on the singular case in which p is close to 1. Pointwise estimates for solutions and their full or fractional derivatives are deduced from such comparison estimates.
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报告人：Sibei Yang (Lanzhou University)
题 目：Hardy spaces on non-tangentially accessible domains with applications to global regularity of Dirichlet problems
时 间：2022.08.17（星期三）10:00-11:00
地 点：Zoom ID: 924 888 5804 Passcode: AMSS2022
Join Zoom Meeting :
https://us06web.zoom.us/j/9248885804?pwd=OXg2VDhBT0pxRkd1Z3RJS0NFMnRDdz09
摘 要：Let Ω be a bounded non-tangentially accessible domain of 
. Assume that LD is a second-order divergence form elliptic operator having real-valued, bounded, measurable coefficients on L2(Ω) with the Dirichlet boundary condition. We prove that the Hardy spaces Hpr(Ω)=Hp(Ω)= HpLD(Ω) with equivalent quasi-norms for some p∈(0, 1], where Hpr(Ω) denotes the ‘restricted type’ Hardy space on the domain Ω and HpLD(Ω) the Hardy space associated with LD. As applications, we further obtain the global gradient estimates for the Dirichlet problem of LD in both Lp(Ω), with p∈(1, p0), and Hp(Ω), with p∈(n/n+1,1], where p0∈(2, ∞) is a constant depending on Ω and the coefficient matrix of LD. This talk is based on a joint work with Prof. Dachun Yang.
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