We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type monotonicity formulæ and provides a classification of all possible homogeneity degrees of limiting entire profiles. As a consequence, we establish a strong unique continuation principle from boundary points.

De Luca, A., Felli, V., Vita, S. (2022). Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations. ADVANCES IN MATHEMATICS, 400(14 May 2022) [10.1016/j.aim.2022.108279].

Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations

De Luca, Alessandra
;
Felli, Veronica
;
Vita, Stefano
2022

Abstract

We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type monotonicity formulæ and provides a classification of all possible homogeneity degrees of limiting entire profiles. As a consequence, we establish a strong unique continuation principle from boundary points.
Articolo in rivista - Articolo scientifico
Boundary behaviour of solutions; Fractional elliptic equations; Monotonicity formula; Unique continuation;
English
De Luca, A., Felli, V., Vita, S. (2022). Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations. ADVANCES IN MATHEMATICS, 400(14 May 2022) [10.1016/j.aim.2022.108279].
De Luca, A; Felli, V; Vita, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/355995
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