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arXiv · 2407.18830

A note on geometric assumptions for unique continuation from the edge of a crack

Alessandra De Luca
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Abstract

The present paper aims at representing an improvement of the result in [2], where a strong unique continuation property and a description of the local behaviour around the edge of a crack for solutions to an elliptic problem are established, by relaxing the star-shapedness condition on the complement of the crack. More specifically, this assumption will be dropped off by applying a suitable diffeomorphism which straightens the boundary of the crack, before performing the approximation procedure developed in [2] in order to derive a suitable monotonicity formula. This will yield the appearence of a matrix in the equation, which shall be handled appropriately: for this we will take a hint from [4].

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Alessandra De Luca. 2024-07-26. A note on geometric assumptions for unique continuation from the edge of a crack. https://arxiv.org/abs/2407.18830

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