We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients.We also present a sharp comparison with the ...We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients.We also present a sharp comparison with the corresponding Green5s function for constant coefficients equations.展开更多
We give an alternative proof of a recent result in[1]by Caffarelli,Soria-Carro,and Stinga about the C^(1,α)regularity of weak solutions to transmission problems with C^(1,α)interfaces.Our proof does not use the mean...We give an alternative proof of a recent result in[1]by Caffarelli,Soria-Carro,and Stinga about the C^(1,α)regularity of weak solutions to transmission problems with C^(1,α)interfaces.Our proof does not use the mean value property or the maximum principle,and also works for more general elliptic systems with variable coefficients.This answers a question raised in[1].Some extensions to C^(1,Dini)interfaces and to domains with multiple sub-domains are also discussed.展开更多
基金partially supported by National Research Foundation of Korea(NRF)Grant No.NRF-2019R1A2C2002724 and No.NRF-20151009350.
文摘We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients.We also present a sharp comparison with the corresponding Green5s function for constant coefficients equations.
基金supported by the Simons Foundation,grant No.709545。
文摘We give an alternative proof of a recent result in[1]by Caffarelli,Soria-Carro,and Stinga about the C^(1,α)regularity of weak solutions to transmission problems with C^(1,α)interfaces.Our proof does not use the mean value property or the maximum principle,and also works for more general elliptic systems with variable coefficients.This answers a question raised in[1].Some extensions to C^(1,Dini)interfaces and to domains with multiple sub-domains are also discussed.
