International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 5, Pages 217-238
Resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces
Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, Espoo 02015 HUT, Finland
Received 25 March 2003
Copyright © 2004 Nikolai Yu. Bakaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.