Positivity of elliptic difference operators and its applications

Author(s):  
Galina E. Semenova
2002 ◽  
Vol 132 (6) ◽  
pp. 1395-1406 ◽  
Author(s):  
Hung-Ju Kuo ◽  
Neil S. Trudinger

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.


2018 ◽  
Vol 265 (8) ◽  
pp. 3709-3753
Author(s):  
Alexandre B. Simas ◽  
Fábio J. Valentim

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

Sign in / Sign up

Export Citation Format

Share Document