Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data

Giovanni Alessandrini; Maarten V. De Hoop; Romina Gaburro; Eva Sincich

doi:10.3233/ASY-171457

Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data

Giovanni Alessandrini
, Maarten V. De Hoop
, Romina Gaburro
, Eva Sincich

Department of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the inverse boundary value problem of determining the potential q in the equation u + qu = 0 in Rn, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension n 3 for potentials that are piecewise linear on a given partition of No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation u + k2c -2u = 0 at fixed frequency k.

Original language	English
Pages (from-to)	115-149
Number of pages	35
Journal	Asymptotic Analysis
Volume	108
Issue number	3
DOIs	https://doi.org/10.3233/ASY-171457
Publication status	Published - 2018

Keywords

Cauchy data
Full Waveform Inversion
Green's function
Lipschitz stability

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10.3233/ASY-171457

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abstract = "We consider the inverse boundary value problem of determining the potential q in the equation u + qu = 0 in Rn, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension n 3 for potentials that are piecewise linear on a given partition of No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation u + k2c -2u = 0 at fixed frequency k.",

keywords = "Cauchy data, Full Waveform Inversion, Green's function, Lipschitz stability",

author = "Giovanni Alessandrini and \{De Hoop\}, \{Maarten V.\} and Romina Gaburro and Eva Sincich",

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journal = "Asymptotic Analysis",

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T1 - Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data

AU - Alessandrini, Giovanni

AU - De Hoop, Maarten V.

AU - Gaburro, Romina

AU - Sincich, Eva

PY - 2018

Y1 - 2018

N2 - We consider the inverse boundary value problem of determining the potential q in the equation u + qu = 0 in Rn, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension n 3 for potentials that are piecewise linear on a given partition of No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation u + k2c -2u = 0 at fixed frequency k.

AB - We consider the inverse boundary value problem of determining the potential q in the equation u + qu = 0 in Rn, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension n 3 for potentials that are piecewise linear on a given partition of No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation u + k2c -2u = 0 at fixed frequency k.

KW - Cauchy data

KW - Full Waveform Inversion

KW - Green's function

KW - Lipschitz stability

UR - https://www.scopus.com/pages/publications/85048723237

U2 - 10.3233/ASY-171457

DO - 10.3233/ASY-171457

M3 - Article

AN - SCOPUS:85048723237

SN - 0921-7134

VL - 108

SP - 115

EP - 149

JO - Asymptotic Analysis

JF - Asymptotic Analysis

IS - 3

ER -

Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data

Abstract

Keywords

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