Discrete Interior Schauder Estimates for Elliptic Difference Operators

1968 ◽  
Vol 5 (3) ◽  
pp. 626-645 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Difference Operators ◽  
Schauder Estimates ◽  
Elliptic Difference

Schauder estimates for fully nonlinear elliptic difference operators

2002 ◽  
Vol 132 (6) ◽  
pp. 1395-1406 ◽  
Author(s):  
Hung-Ju Kuo ◽  
Neil S. Trudinger
Keyword(s):  
Elliptic Partial Differential Equations ◽  
Difference Operators ◽  
Pointwise Estimates ◽  
Fully Nonlinear ◽  
Schauder Estimates ◽  
Elliptic Difference ◽  
Nonlinear Elliptic ◽  
Special Case ◽  
General Meshes ◽  
Hölder Estimates

In this paper, we are concerned with discrete Schauder estimates for solutions of fully nonlinear elliptic difference equations. Our estimates are discrete versions of second derivative Hölder estimates of Evans, Krylov and Safonov for fully nonlinear elliptic partial differential equations. They extend previous results of Holtby for the special case of functions of pure second-order differences on cubic meshes. As with Holtby's work, the fundamental ingredients are the pointwise estimates of Kuo-Trudinger for linear difference schemes on general meshes.

scholarly journals Homogenization of generalized second-order elliptic difference operators

2018 ◽  
Vol 265 (8) ◽  
pp. 3709-3753
Author(s):  
Alexandre B. Simas ◽  
Fábio J. Valentim
Keyword(s):  
Second Order ◽  
Difference Operators ◽  
Elliptic Difference

Homogenization of Elliptic Difference Operators

2001 ◽  
Vol 33 (1) ◽  
pp. 53-83 ◽  
Author(s):  
Andrey Piatnitski ◽  
Elisabeth Remy
Keyword(s):  
Difference Operators ◽  
Elliptic Difference

scholarly journals Nonlinear Beltrami operators, Schauder estimates and bounds for the Jacobian

2017 ◽  
Vol 34 (6) ◽  
pp. 1543-1559 ◽  
Author(s):  
Kari Astala ◽  
Albert Clop ◽  
Daniel Faraco ◽  
Jarmo Jääskeläinen ◽  
Aleksis Koski
Keyword(s):  
Schauder Estimates
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