In this short Note we give a self-contained example of a consistent family of holomorphic semigroups such that does not have maximal regularity for . This answers negatively the open question whether maximal regularity extrapolates from to the -scale.
Dans cette Note, nous démontrons lʼexistence dʼune famille de semi-groupes holomorphes telle que nʼa pas la régularité maximale pour . De cette façon, nous répondons négativement à la question ouverte qui consiste à savoir si la régularité maximale extrapole entre et .
Accepted:
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Stephan Fackler 1
@article{CRMATH_2013__351_1-2_53_0, author = {Stephan Fackler}, title = {An explicit counterexample for the $ {L}^{p}$-maximal regularity problem}, journal = {Comptes Rendus. Math\'ematique}, pages = {53--56}, publisher = {Elsevier}, volume = {351}, number = {1-2}, year = {2013}, doi = {10.1016/j.crma.2013.01.013}, language = {en}, }
Stephan Fackler. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.01.013/
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