In the present paper, which aims at representing an improvement of De Luca and Felli (2021), we prove the validity of the strong unique continuation property for solutions to some second order elliptic equations from the edge of a crack via a description of their local behaviour. In particular we relax the star-shapedness condition on the complement of the crack considered in De Luca and Felli (2021) by applying a suitable diffeomorphism which straightens the boundary of the crack before performing an approximation of the fractured domain needed to derive a monotonicity formula
De Luca, A. (2026). A note on unique continuation from the edge of a crack with no star-shapedness condition. NONLINEAR ANALYSIS, 264(March 2026) [10.1016/j.na.2025.114006].
A note on unique continuation from the edge of a crack with no star-shapedness condition
De Luca A.
2026
Abstract
In the present paper, which aims at representing an improvement of De Luca and Felli (2021), we prove the validity of the strong unique continuation property for solutions to some second order elliptic equations from the edge of a crack via a description of their local behaviour. In particular we relax the star-shapedness condition on the complement of the crack considered in De Luca and Felli (2021) by applying a suitable diffeomorphism which straightens the boundary of the crack before performing an approximation of the fractured domain needed to derive a monotonicity formula
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De Luca-2026-Nonlinear Analysis-VoR.pdf
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Descrizione: A note on unique continuation from the edge of a crack with no star-shapedness condition
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