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Maximal Lp regularity for parabolic difference equations

✍ Scribed by Matthias Geissert

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
174 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this paper, we consider a family of finite difference operators {Ah }~h >0~ on discrete L ~q~ ‐spaces L ~q~ (ℝ^N^ ~h~ ). We show that the solution u ~h~ to u ′~h~ (t) – A ~h~ u ~h~(t) = f ~h~ (t), t > 0, u ~h~ (0) = 0 satisfies the estimate ‖A ~h~ u ~h~ ‖ ≤ C ‖f ~h~ ‖, where C is independent of h and f ~h~ . In this case, the family {A ~h~ }~h >0~ is said to have discrete maximal L ~p~ regularity on the discrete L ~q~ ‐space. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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