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- W4366835583 abstract "A differential operator $T$ satisfies the $L^2$-unique continuation property if every $L^2$-solution of $T$ that vanishes on an open subset vanishes identically. We study the $L^2$-unique continuation property of an operator $T$ acting on a manifold with bounded geometry. In particular, we establish some connections between this property and the regularity properties of $T$. As an application, we prove that the deformation operator on a manifold with bounded geometry satisfies regularity and $L^2$-unique continuation properties. As another application, we prove that suitable elliptic operators are invertible (Hadamard well-posedness). Our results apply to compact manifolds, which have bounded geometry." @default.
- W4366835583 created "2023-04-25" @default.
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- W4366835583 date "2023-04-21" @default.
- W4366835583 modified "2023-10-14" @default.
- W4366835583 title "The $L^2$-unique continuation property on manifolds with bounded geometry and the deformation operator" @default.
- W4366835583 doi "https://doi.org/10.48550/arxiv.2304.10943" @default.
- W4366835583 hasPublicationYear "2023" @default.
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