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.
Lingua originale | Inglese |
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pagine (da-a) | 4133-4190 |
Numero di pagine | 58 |
Rivista | Nonlinearity |
Volume | 33 |
Numero di pubblicazione | 8 |
DOI | |
Stato di pubblicazione | Pubblicato - ago 2020 |