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Discrete Maximal Lp Regularity for Finite Element Operators

✍ Scribed by Geissert, Matthias

Book ID
118189967
Publisher
Society for Industrial and Applied Mathematics
Year
2006
Tongue
English
Weight
307 KB
Volume
44
Category
Article
ISSN
0036-1429

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In the first part of this paper, we give the following interpolation result on the analyticity (i.e. the property &(T&I ) T n & CΓ‚n for all n # N) of an operator T on L p : If T is powerbounded on L p and L q as well as analytic on L p , then T is powerbounded and analytic on L r for all r strictly

Maximal Lp regularity for parabolic diff
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✍ Matthias Geissert πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 174 KB

## 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__ β€²~__h__~ (__t__) – __A__ ~__h__~ __u__ ~h~(__t__) = __f__ ~__h__~ (__t__), __t__