Schrödinger和含陷波方程反问题的稳定性估计

IF 1.3 2区数学 Q1 MATHEMATICS

Revista Matematica Iberoamericana Pub Date : 2021-06-21 DOI:10.4171/rmi/1327

V'ictor Arnaiz, C. Guillarmou

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引用次数: 0

摘要

.对于一类具有边界的黎曼流形，包括所有具有严格凸边界的负曲流形，我们在与Schr¨odinger方程和波动方程相关的Dirichlet到Neumann映射的确定电势或保角因子的几何逆问题中建立了H¨older型稳定性估计。这个结果的新颖之处在于，我们允许一些测地线被困在流形内，并且具有有限的长度。

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Stability estimates in inverse problems for the Schrödinger and wave equations with trapping

. For a class of Riemannian manifolds with boundary that includes all negatively curved manifolds with strictly convex boundary, we establish H¨older type stability estimates in the geometric inverse problem of determining the electric potential or the conformal factor from the Dirichlet-to-Neumann map associated with the Schr¨odinger equation and the wave equation. The novelty in this result lies in the fact that we allow some geodesics to be trapped inside the manifold and have inﬁnite length.

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来源期刊

Revista Matematica Iberoamericana 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.