The Kato Square Root Problem follows from an extrapolation property of the Laplacian
- Autores: Moritz Egert, Robert Haller-Dintelmann, Patrick Tolksdorf
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 60, Nº 2, 2016, págs. 451-483
- Idioma: inglés
- DOI: 10.5565/10.5565/PUBLMAT-60216_05
- Enlaces
-
Resumen
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.
¿Es nuevo? Regístrese
Ventajas de registrarse
