Comparison estimates and pointwise regularity for p-Laplace  equations with measure data

2022.08.17（星期三）09:00-10:00

点：Zoom ID: 924 888 5804  Passcode: AMSS2022

Join Zoom Meeting :

https://us06web.zoom.us/j/9248885804?pwd=OXg2VDhBT0pxRkd1Z3RJS0NFMnRDdz09

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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Hardy spaces on non-tangentially accessible domains with applications to global regularity of Dirichlet problems

2022.08.17（星期三）10:00-11:00

点：Zoom ID: 924 888 5804  Passcode: AMSS2022

Join Zoom Meeting :

https://us06web.zoom.us/j/9248885804?pwd=OXg2VDhBT0pxRkd1Z3RJS0NFMnRDdz09

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.