Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations

Ru-Yu Lai; Laurel Ohm

doi:10.3934/ipi.2021051

Article Contents

2022, Volume 16, Issue 2: 305-323. Doi: 10.3934/ipi.2021051

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Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations

Ru-Yu Lai^1, and
Laurel Ohm^2,

1.
School of Mathematics, University of Minnesota, USA
2.
Courant Institute, New York University, USA

Received: February 2021

Revised: May 2021

Early access: July 2021

Published: April 2022

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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.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35R11.

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References

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