Maximum Norm Regularity of Periodic Elliptic Difference Operators With Variable Coefficients∗
Revised: 25 February 2015
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.
Mathematics Subject Classification: 65N06
Key words: Elliptic / finite difference / variable coefficients / periodic boundary conditions
© EDP Sciences, SMAI 2015