We prove regularity results for divergence form periodic second order elliptic difference operators on the space of functions of mean value zero, valid in maximum norm. The estimates obtained are discrete analogues of the regularity results for continuous operators. The maximum norms of the inverse of such an elliptic operator and of its first spatial differences are uniformly bounded in the grid spacing, and second spatial differences are uniformly bounded except for a logarithmic factor in the grid spacing.
DOI : 10.1051/m2an/2015018
Mots-clés : Elliptic, finite difference, variable coefficients, periodic boundary conditions
@article{M2AN_2015__49_5_1451_0,
author = {Pruitt, Michael},
title = {Maximum {Norm} {Regularity} of {Periodic} {Elliptic} {Difference} {Operators} {With} {Variable} {Coefficients}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1451--1461},
publisher = {EDP-Sciences},
volume = {49},
number = {5},
year = {2015},
doi = {10.1051/m2an/2015018},
zbl = {1360.65262},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2015018/}
}
TY - JOUR AU - Pruitt, Michael TI - Maximum Norm Regularity of Periodic Elliptic Difference Operators With Variable Coefficients JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 1451 EP - 1461 VL - 49 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015018/ DO - 10.1051/m2an/2015018 LA - en ID - M2AN_2015__49_5_1451_0 ER -
%0 Journal Article %A Pruitt, Michael %T Maximum Norm Regularity of Periodic Elliptic Difference Operators With Variable Coefficients %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 1451-1461 %V 49 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015018/ %R 10.1051/m2an/2015018 %G en %F M2AN_2015__49_5_1451_0
Pruitt, Michael. Maximum Norm Regularity of Periodic Elliptic Difference Operators With Variable Coefficients. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1451-1461. doi : 10.1051/m2an/2015018. http://www.numdam.org/articles/10.1051/m2an/2015018/
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