The L 2 -unique continuation property on manifolds with bounded geometry and the deformation operator
Year: 2025
Type: article
Abstract: By definition, a differential operator T on a connected manifold satisfies the L 2 {L^{2}} -unique continuation property if every L 2 {L^{2}} -solution of T that vanishes on an open subset vanishes identically. We study the L 2 {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 {L^{2}} -unique continuation properties. As another application, we prove that suitable elliptic operators are invertible (Hadamard well-posedness). Our results apply, in particular, to compact manifolds, as all such manifolds have bounded geometry.
Source: Forum Mathematicum
Authors: Nadine Große, Mirela Kohr, Victor Nistor
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409874062