International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 5-8, Pages 217-238
doi:10.1155/S0161171204303200

Resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces

Abstract

We present some resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces, for which the first space in a pair is endowed with stronger norm. In this work we deal with estimates in (Lebesgue, Lebesgue), (Hölder, Lebesgue), and (Hölder, Hölder) pairs of norms. In particular, our results are useful for the stability and error analysis of semidiscrete and fully discrete approximations to parabolic partial differential problems with rough and distribution-valued data.