Unique continuation principles for a higher order fractional Laplace equation

Veronica Felli, Alberto Ferrero

Risultato della ricerca: Contributo su rivistaArticolo in rivistapeer review

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 originaleInglese
pagine (da-a)4133-4190
Numero di pagine58
RivistaNonlinearity
Volume33
Numero di pubblicazione8
DOI
Stato di pubblicazionePubblicato - ago 2020

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