In this paper we prove the strong unique continuation principle and the unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the Caffarelli-Silvestre (2007 Commun. PDE 32 1245-60) extension method combined with an Almgren type monotonicity formula. The corresponding extended problem is formulated as a system of two second order equations with singular or degenerate weights in a half-space, for which asymptotic estimates are derived by a blow-up analysis.
Felli, V., Ferrero, A. (2020). Unique continuation principles for a higher order fractional Laplace equation. NONLINEARITY, 33(8), 4133-4190 [10.1088/1361-6544/ab8691].
Unique continuation principles for a higher order fractional Laplace equation
Felli V.
;
2020
Abstract
In this paper we prove the strong unique continuation principle and the unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the Caffarelli-Silvestre (2007 Commun. PDE 32 1245-60) extension method combined with an Almgren type monotonicity formula. The corresponding extended problem is formulated as a system of two second order equations with singular or degenerate weights in a half-space, for which asymptotic estimates are derived by a blow-up analysis.
| File | Dimensione | Formato | |
|---|---|---|---|
|
Fall-2020-Nonlinearity-AAM.pdf
accesso aperto
Descrizione: Article
Tipologia di allegato:
Author’s Accepted Manuscript, AAM (Post-print)
Licenza:
Creative Commons
Dimensione
639.5 kB
Formato
Adobe PDF
|
639.5 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
