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Baillon's Theorem on Maximal Regularity

✍ Scribed by B. Eberhardt; G. Greiner

Publisher
Springer Netherlands
Year
1992
Tongue
English
Weight
356 KB
Volume
27
Category
Article
ISSN
0167-8019

No coin nor oath required. For personal study only.

✦ Synopsis

The aim of this note is to give a proof of Baillon's Theorem on Maximal Regularity.

Though it is in some sense a negative result (it states that for abstract Cauchy problems maximal regularity can occur only in very special cases), it is commonly accepted that it is important. Many people believe that its proof is very complicated. This might be due to the fact that Baillon's note in the Comptes Rendus is rather short and sometimes difficult to understand. The proof outlined here follows basically Baillon's lines. However it is simplified and (hopefully) easier to understand.

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graphs of order n and size at least t r (n) that do not have a vertex x of maximal degree d x whose neighbours span at least t r&1 (d x )+1 edges. Furthermore, we show that, for every graph G of order n and size at least t r (n), the degree-greedy algorithm used by Bondy (1983, J. Combin. Theory Ser