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.
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