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ArticleOriginal scientific text

Title

On coerciveness in Besov spaces for abstract parabolic equations of higher order

Authors 1

Affiliations

  1. Department of Applied Physics, Faculty of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan

Abstract

We are concerned with a relation between parabolicity and coerciveness in Besov spaces for a higher order linear evolution equation in a Banach space. As proved in a preceding work, a higher order linear evolution equation enjoys coerciveness in Besov spaces under a certain parabolicity condition adopted and studied by several authors. We show that for a higher order linear evolution equation coerciveness in Besov spaces forces the parabolicity of the equation. We thus conclude that parabolicity and coerciveness in Besov spaces are equivalent.

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Studia Mathematica
1999/134/1
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Pages:
79-98
Main language of publication
English
Received
1998-04-08
Accepted
1998-06-10
Published
1999
Exact and natural sciences