The Kato Square Root Problem follows from an extrapolation property of the Laplacian
Egert, Moritz (Université Paris-Sud. Laboratoire de Mathématiques d'Orsay)
Haller-Dintelmann, Robert (Technische Universität Darmstadt. Fachbereich Mathematik)
Tolksdorf, Patrick (Technische Universität Darmstadt. Fachbereich Mathematik)

Date:	2016
Abstract:	On a domain Ω ⊆ _ Rd we consider second-order elliptic systems in divergence-form with bounded complex coefficients, realized via a sesquilinear form with domain H1/0 (Ω) ⊆ V ⊆ H1 (Ω). Under very mild assumptions on Ω and V we show that the solution to the Kato Square Root Problem for such systems can be deduced from a regularity result for the fractional powers of the negative Laplacian in the same geometric setting. This extends earlier results of McIntosh [25] and Axelsson-Keith-McIntosh [6] to non-smooth coefficients and domains.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Kato's square root problem ; Sectorial and bisectorial operators ; Functional calculus ; Quadratic estimates ; Carleson measures
Published in:	Publicacions matemàtiques, Vol. 60 Núm. 2 (2016) , p. 451-483 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/311012
DOI: 10.5565/PUBLMAT_60216_05

33 p, 487.6 KB

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