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)

Data: 2016
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Kato's square root problem ; Sectorial and bisectorial operators ; Functional calculus ; Quadratic estimates ; Carleson measures
Publicat a: Publicacions matemàtiques, Vol. 60 Núm. 2 (2016) , p. 451-483 (Articles) , ISSN 2014-4350

Adreça original:
DOI: 10.5565/PUBLMAT-60216_05
DOI: 10.5565/10.5565/PUBLMAT-60216_05

33 p, 487.6 KB

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