scholarly journals Homogenization of high order elliptic operators with periodic coefficients

2016 ◽  
Vol 28 (1) ◽  
pp. 65-108 ◽  
Author(s):  
A. A. Kukushkin ◽  
T. A. Suslina
Keyword(s):  
Elliptic Operators ◽  
High Order ◽  
Periodic Coefficients

scholarly journals High Order Fefferman-Phong Type Inequalities in Carnot Groups and Regularity for Degenerate Elliptic Operators plus a Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Pengcheng Niu ◽  
Kelei Zhang
Keyword(s):  
Euclidean Space ◽  
Vector Fields ◽  
Carnot Group ◽  
A Priori ◽  
Elliptic Operators ◽  
High Order ◽  
Carnot Groups ◽  
Degenerate Elliptic Operators ◽  
Degenerate Elliptic ◽  
Horizontal Vector

Let{X1,X2,…,Xm}be the basis of space of horizontal vector fields in a Carnot groupG=(Rn;∘) (m<n). We prove high order Fefferman-Phong type inequalities inG. As applications, we derive a prioriLp(G)estimates for the nondivergence degenerate elliptic operatorsL=-∑i,j=1maij(x)XiXj+V(x)withVMOcoefficients and a potentialVbelonging to an appropriate Stummel type class introduced in this paper. Some of our results are also new even for the usual Euclidean space.

scholarly journals Spectral approximation of elliptic operators by the Hybrid High-Order method

2018 ◽  
Vol 88 (318) ◽  
pp. 1559-1586 ◽  
Author(s):  
Victor Calo ◽  
Matteo Cicuttin ◽  
Quanling Deng ◽  
Alexandre Ern
Keyword(s):  
Elliptic Operators ◽  
High Order ◽  
Spectral Approximation ◽  
Order Method ◽  
High Order Method
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