INVERSE PROBLEMS FOR THE FRACTIONAL LAPLACE EQUATION WITH LOWER ORDER NONLINEAR PERTURBATIONS

Ru Yu Lai; Laurel Ohm

doi:10.3934/ipi.2021051

INVERSE PROBLEMS FOR THE FRACTIONAL LAPLACE EQUATION WITH LOWER ORDER NONLINEAR PERTURBATIONS

Ru Yu Lai, Laurel Ohm

School of Mathematics

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

7 Scopus citations

Abstract

We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinearities can be uniquely determined from exterior measurements under suitable settings.

Original language	English (US)
Pages (from-to)	305-323
Number of pages	19
Journal	Inverse Problems and Imaging
Volume	16
Issue number	2
DOIs	https://doi.org/10.3934/ipi.2021051
State	Published - Feb 2022

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© 2022, American Institute of Mathematical Sciences. All rights reserved.

Keywords

Fractional Laplacian
Inverse problems
Nonlinear perturbations

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10.3934/ipi.2021051

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title = "INVERSE PROBLEMS FOR THE FRACTIONAL LAPLACE EQUATION WITH LOWER ORDER NONLINEAR PERTURBATIONS",

abstract = "We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinearities can be uniquely determined from exterior measurements under suitable settings.",

keywords = "Fractional Laplacian, Inverse problems, Nonlinear perturbations",

author = "Lai, {Ru Yu} and Laurel Ohm",

year = "2022",

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publisher = "American Institute of Mathematical Sciences",

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N2 - We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinearities can be uniquely determined from exterior measurements under suitable settings.

AB - We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinearities can be uniquely determined from exterior measurements under suitable settings.

KW - Fractional Laplacian

KW - Inverse problems

KW - Nonlinear perturbations

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INVERSE PROBLEMS FOR THE FRACTIONAL LAPLACE EQUATION WITH LOWER ORDER NONLINEAR PERTURBATIONS

Abstract

Bibliographical note

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