Geodesic
Maximum Norm Regularity of Periodic Elliptic Difference Operators With Variable Coefficients
Pruitt, Michael1
1 University of Connecticut, USA.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1451-1461

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
DOI : 10.1051/m2an/2015018
Classification : 65N06
Keywords: Elliptic, finite difference, variable coefficients, periodic boundary conditions

Pruitt, Michael 1

1 University of Connecticut, USA. 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :