Weighted mixed-norm $L_p$-estimates for elliptic and parabolic equations in non-divergence form with singular coefficients

2020 ◽  
Author(s):  
Hongjie Dong ◽  
Tuoc Phan
Keyword(s):  
Parabolic Equations ◽  
Divergence Form ◽  
Mixed Norm ◽  
Singular Coefficients ◽  
Elliptic And Parabolic Equations

scholarly journals Partial Schauder Estimates for Second-Order Elliptic and Parabolic Equations: A Revisit

2017 ◽  
Vol 2019 (7) ◽  
pp. 2085-2136 ◽  
Author(s):  
Hongjie Dong ◽  
Seick Kim
Keyword(s):  
Parabolic Equations ◽  
Divergence Form ◽  
Second Order ◽  
The Other ◽  
Schauder Estimates ◽  
Independent Variables ◽  
Elliptic And Parabolic Equations

AbstractUnder various conditions, we establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving Hölder semi-norms not with respect to all, but only with respect to some of the independent variables. A novelty of our results is that the coefficients are allowed to be merely measurable with respect to the other independent variables.

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