Partial Differential Equations/Functional Analysis
An explicit counterexample for the Lp-maximal regularity problem
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 53-56.

In this short Note we give a self-contained example of a consistent family of holomorphic semigroups (Tp(t))t0 such that (Tp(t))t0 does not have maximal regularity for p>2. This answers negatively the open question whether maximal regularity extrapolates from L2 to the Lp-scale.

Dans cette Note, nous démontrons lʼexistence dʼune famille de semi-groupes holomorphes (Tp(t))t0 telle que (Tp(t))t0 nʼa pas la régularité maximale pour p>2. De cette façon, nous répondons négativement à la question ouverte qui consiste à savoir si la régularité maximale extrapole entre L2 et Lp.

Published online:
DOI: 10.1016/j.crma.2013.01.013
Fackler, Stephan 1

1 Institute of Applied Analysis, University of Ulm, Helmholtzstraße 18, 89069 Ulm, Germany
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     title = {An explicit counterexample for the $ {L}^{p}$-maximal regularity problem},
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Fackler, Stephan. An explicit counterexample for the $ {L}^{p}$-maximal regularity problem. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 53-56. doi : 10.1016/j.crma.2013.01.013.

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