A note on boundary differentiability of solutions of elliptic equations in nondivergence form

2019 ◽  
Vol 162 (3-4) ◽  
pp. 305-313
Author(s):  
Yongpan Huang ◽  
Dongsheng Li ◽  
Lihe Wang
Keyword(s):  
Elliptic Equations ◽  
Nondivergence Form ◽  
Differentiability Of Solutions

On weighted W2,p estimates for elliptic equations with BMO coefficients in nondivergence form

2015 ◽  
Vol 26 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Sun-Sig Byun ◽  
Mikyoung Lee
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nondivergence Form ◽  
Muckenhoupt Class ◽  
The Matrix ◽  
Bmo Coefficients

We establish global weighted W2,p, 2 < p < ∞, estimates for the solution to the Dirichlet problem for an elliptic equation in nondivergence form with BMO coefficients in a C1,1 domain under the assumption that the matrix of the coefficients has a small BMO semi-norm while the associated weight belongs to a Muckenhoupt class. These conditions are weaker than those reported in the literature.

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