A family of physics-based preconditioners for solving elliptic equations on highly heterogeneous media

2009 ◽  
Vol 59 (6) ◽  
pp. 1159-1186 ◽  
Author(s):  
Burak Aksoylu ◽  
Hector Klie
Keyword(s):  
Elliptic Equations ◽  
Heterogeneous Media

scholarly journals A multiscale model reduction method for nonlinear monotone elliptic equations in heterogeneous media

2017 ◽  
Vol 12 (4) ◽  
pp. 619-642 ◽  
Author(s):  
Eric Chung ◽  
◽  
Yalchin Efendiev ◽  
Ke Shi ◽  
Shuai Ye ◽  
...  
Keyword(s):  
Model Reduction ◽  
Elliptic Equations ◽  
Heterogeneous Media ◽  
Reduction Method ◽  
Multiscale Model

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

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