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Maximal L p regularity for parabolic difference equations
Author(s) -
Geissert Matthias
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410455
Subject(s) - mathematics , space (punctuation) , combinatorics , mathematical physics , philosophy , linguistics
In this paper, we consider a family of finite difference operators { Ah } h >0 on discrete L q ‐spaces L q (ℝ Nh ). 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 ‖ L p(ℝ + ; L q(ℝ N h))≤ C ‖ f h ‖ L p(ℝ + ; L q(ℝ N 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)