Inverse boundary problems: toward a unified theory

Uniqueness and reconstruction for the fractional Calderón problem with a single measurement

Author(s): Tuhin Ghosh, Angkana Rüland, Mikko Salo, Gunther Uhlmann
Published in: Journal of Functional Analysis, Issue 279/1, 2020, Page(s) 108505, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2020.108505

Jacobian of solutions to the conductivity equation in limited view

Author(s): Mikko Salo; Hjørdis Schlüter
Published in: Inverse Problems, Issue Volume 39, Number 2, 2023, Page(s) 025001, ISSN 1361-6420
Publisher: Institute of Physics
DOI: 10.1088/1361-6420/aca904

Fixed angle inverse scattering for sound speeds close to constant

Author(s): Ma, Shiqi; Potenciano-Machado, Leyter; Salo, Mikko
Published in: SIAM Journal on Mathematical Analysis, Issue 55, 2023, ISSN 1095-7154
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m147640x

Inverse problems for semilinear elliptic PDE with measurements at a single point

Author(s): Mikko Salo, Leo Tzou
Published in: Proceedings of the American Mathematical Society, Issue Volume 151, 2023, Page(s) 2023-2030, ISSN 1088-6826
Publisher: American Mathematical Society
DOI: 10.1090/proc/16255

Refined instability estimates for some inverse problems

Author(s): Pu-Zhao Kow; Jenn-Nan Wang
Published in: Inverse Problems and Imaging, Issue 16, 2022, Page(s) 1619-1642, ISSN 1930-8337
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/ipi.2022017

Inverse problems for a fractional conductivity equation

Author(s): Giovanni Covi
Published in: Nonlinear Analysis, Issue 193, 2020, Page(s) 111418, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2019.01.008

An inverse problem for semilinear equations involving the fractional Laplacian

Author(s): Pu-Zhao Kow, Shiqi Ma, Suman Kumar Sahoo
Published in: Inverse Problems, Issue Volume 39, Number 9, 2023, Page(s) 095006, ISSN 1361-6420
Publisher: Institute of Physics
DOI: 10.1088/1361-6420/ace9f4

On some partial data Calderón type problems with mixed boundary conditions

Author(s): Giovanni Covi, Angkana Rüland
Published in: Journal of Differential Equations, Issue 288, 2021, Page(s) 141-203, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2021.04.004

The fixed angle scattering problem with a first order perturbation

Author(s): Cristóbal J. Meroño, Leyter Potenciano-Machado, Mikko Salo
Published in: Annales Henri Poincaré, Issue 22, 2021, Page(s) 3699–3746, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-021-01081-w

Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena

Author(s): Pu-Zhao Kow, Simon Larson, Mikko Salo, Henrik Shahgholian
Published in: Potential Analysis, 2023, ISSN 1572-929X
Publisher: Springer
DOI: 10.1007/s11118-022-10054-5

The linearized Calderón problem for polyharmonic operators

Author(s): Suman Kumar Sahoo, Mikko Salo
Published in: Journal of Differential Equations, Issue Volume 360, 2023, Page(s) 407-451, ISSN 1090-2732
Publisher: Elsevier
DOI: 10.1016/j.jde.2023.03.017

Uniqueness in an inverse problem of fractional elasticity

Author(s): Giovanni Covi, Maarten de Hoop, Mikko Salo
Published in: Proceedings of the Royal Society A, Issue Volume 479, issue 2278, 2023, Page(s) 20230474, ISSN 1471-2946
Publisher: Royal Society
DOI: 10.1098/rspa.2023.0474

Linearized Calder\'on problem and exponentially accurate quasimodes for analytic manifolds

Author(s): Krupchyk, Katya; Liimatainen, Tony; Salo, Mikko
Published in: Advances in Mathematics, Issue 402, 2022, Page(s) 108362, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108362

The Calderón problem for the fractional Schrödinger equation

Author(s): Tuhin Ghosh; Mikko Salo; Gunther Uhlmann
Published in: Analysis & PDE, Issue Vol. 13, no. 2, 2020, Page(s) 455-475, ISSN 1948-206X
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2020.13.455

Inverse problems for elliptic equations with fractional power type nonlinearities

Author(s): Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko; Tyni, Teemu
Published in: Journal of Differential Equations, Issue 306, 2021, Page(s) 189-219, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2021.10.015

Fixed angle inverse scattering in the presence of a Riemannian metric

Author(s): Ma, Shiqi; Salo, Mikko
Published in: Journal of Inverse and Ill-posed Problems, Issue 30, 2021, Page(s) 495-520, ISSN 1569-3945
Publisher: De Gruyter
DOI: 10.1515/jiip-2020-0119

Unique Continuation Results for Certain Generalized Ray Transforms of Symmetric Tensor Fields

Author(s): Divyansh Agrawal; Venkateswaran P. Krishnan; Suman Kumar Sahoo
Published in: Journal of Geometric Analysis, Issue 32, 2022, Page(s) 245, ISSN 1050-6926
Publisher: American Mathematical Society
DOI: 10.1007/s12220-022-00981-5

The higher order fractional Calderón problem for linear local operators: uniqueness

Author(s): Giovanni Covi, Keijo Mönkkönen, Jesse Railo, Gunther Uhlmann
Published in: Advances in Mathematics, Issue 399, 2022, Page(s) 108246, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108246

Inverse problems for some fractional equations with general nonlinearity

Author(s): Pu-Zhao Kow; Jenn-Nan Wang
Published in: Research in the Mathematical Sciences, Issue Volume 10, 2023, Page(s) 45, ISSN 2197-9847
Publisher: Springer
DOI: 10.1007/s40687-023-00409-8

Free boundary methods and non-scattering phenomena

Author(s): Mikko Salo; Henrik Shahgholian
Published in: Research in the Mathematical Sciences, Issue 13, 2021, ISSN 2522-0144
Publisher: Springer
DOI: 10.48550/arxiv.2106.15154

Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities

Author(s): Shuai Lu; Mikko Salo; Boxi Xu
Published in: Inverse Problems, Issue 38, 2022, Page(s) 065009, ISSN 0266-5611
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6420/ac637a

The Poisson embedding approach to the Calderón problem

Author(s): Matti Lassas, Tony Liimatainen, Mikko Salo
Published in: Mathematische Annalen, Issue 377/1-2, 2020, Page(s) 19-67, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-019-01818-3

Resolvent estimates for the magnetic Schrödinger operator in dimensions $$\ge 2$$≥2

Author(s): Cristóbal J. Meroño, Leyter Potenciano-Machado, Mikko Salo
Published in: Revista Matemática Complutense, 2019, ISSN 1139-1138
Publisher: Universidad Complutense de Madrid
DOI: 10.1007/s13163-019-00316-z

Dimension Bounds in Monotonicity Methods for the Helmholtz Equation

Author(s): Bastian Harrach, Valter Pohjola, Mikko Salo
Published in: SIAM Journal on Mathematical Analysis, Issue 51/4, 2019, Page(s) 2995-3019, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1240708

The Linearized Calderón Problem on Complex Manifolds

Author(s): Colin Guillarmou, Mikko Salo, Leo Tzou
Published in: Acta Mathematica Sinica, English Series, Issue 35/6, 2019, Page(s) 1043-1056, ISSN 1439-8516
Publisher: Springer Verlag
DOI: 10.1007/s10114-019-8129-7

The fixed angle scattering problem and wave equation inverse problems with two measurements

Author(s): R Rakesh, Mikko Salo
Published in: Inverse Problems, 2019, ISSN 0266-5611
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6420/ab23a2

Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations

Author(s): Rakesh, Mikko Salo
Published in: SIAM Journal on Mathematical Analysis, Issue 52/6, 2020, Page(s) 5467-5499, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1319309

Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems

Author(s): Giovanni Covi, Keijo Mönkkönen, Jesse Railo
Published in: Inverse Problems and Imaging, Issue 15, 2021, Page(s) 641-681, ISSN 1930-8345
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/ipi.2021009

A sharp stability estimate for tensor tomography in non-positive curvature

Author(s): Gabriel P. Paternain, Mikko Salo
Published in: Mathematische Zeitschrift, 2020, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-020-02638-x

On Positivity Sets for Helmholtz Solutions

Author(s): Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
Published in: Vietnam Journal of Mathematics, Issue Volume 51, 2023, Page(s) 985-994, ISSN 2305-2228
Publisher: Springer
DOI: 10.1007/s10013-023-00646-y

Momentum Ray Transforms and a Partial Data Inverse Problem for a Polyharmonic Operator

Author(s): Sombuddha Bhattacharyya; Venkateswaran P. Krishnan; Suman K. Sahoo
Published in: SIAM Journal on Mathematical Analysis, Issue Volume 55, Issue 4, 2023, ISSN 1095-7154
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1500617

An inverse problem for the fractional Schrödinger equation in a magnetic field

Author(s): Giovanni Covi
Published in: Inverse Problems, Issue 36/4, 2020, Page(s) 045004, ISSN 0266-5611
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6420/ab661a

Landis-type conjecture for the half-Laplacian

Author(s): Pu-Zhao Kow, Jenn-Nan Wang
Published in: Proceedings of the American Mathematical Society, Issue Volume 151, 2023, Page(s) 2951-2962, ISSN 1088-6826
Publisher: American Mathematical Society
DOI: 10.1090/proc/16093

On instability mechanisms for inverse problems

Author(s): Herbert Koch, Angkana Rüland, Mikko Salo
Published in: Ars Inveniendi Analytica, Issue 7, 2021, ISSN 2769-8505
Publisher: Ars Inveniendi
DOI: 10.15781/c93s-pk62

The fractional Calderón problem: Low regularity and stability

Author(s): Angkana Rüland, Mikko Salo
Published in: Nonlinear Analysis, Issue 193, 2020, Page(s) 111529, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2019.05.010

Applications of Microlocal Analysis in Inverse Problems

Author(s): Mikko Salo
Published in: Mathematics, Issue 8/7, 2020, Page(s) 1184, ISSN 2227-7390
Publisher: MDPI
DOI: 10.3390/math8071184

Limiting Carleman weights and conformally transversally anisotropic manifolds

Author(s): Pablo Angulo, Daniel Faraco, Luis Guijarro, Mikko Salo
Published in: Transactions of the American Mathematical Society, Issue 373/7, 2020, Page(s) 5171-5197, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8072

Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations

Author(s): Matti Lassas, Tony Liimatainen, Yi-Hsuan Lin, Mikko Salo
Published in: Revista Matemática Iberoamericana, Issue 37/4, 2021, Page(s) 1553-1580, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1242

Inverse problems for elliptic equations with power type nonlinearities

Author(s): Matti Lassas, Tony Liimatainen, Yi-Hsuan Lin, Mikko Salo
Published in: Journal de Mathématiques Pures et Appliquées, Issue 145, 2021, Page(s) 44-82, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2020.11.006

Geometric inverse problems

Author(s): Gabriel P. Paternain; Mikko Salo; Gunther Uhlmann
Published in: Cambridge Studies in Advanced Mathematics, Issue 204, 2023, ISBN 9781009039901
Publisher: Cambridge University Press
DOI: 10.1017/9781009039901

A general support theorem for analytic double fibration transforms

Author(s): Mazzucchelli, Marco; Salo, Mikko; Tzou, Leo
Published in: 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2306.05906

Inverse problems for real principal type operators

Author(s): Oksanen, Lauri; Salo, Mikko; Stefanov, Plamen; Uhlmann, Gunther
Published in: 2020
Publisher: arXiv

Unique determination of anisotropic perturbations of a polyharmonic operator from partial boundary data

Author(s): Bhattacharyya, Sombuddha; Krishnan, Venkateswaran P.; Sahoo, Suman Kumar
Published in: 2021
Publisher: arXiv
DOI: 10.48550/arxiv.2111.07610

On scattering behavior of corner domains with anisotropic inhomogeneities

Author(s): Kow, Pu-Zhao; Salo, Mikko; Shahgholian, Henrik
Published in: 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2309.11213

Linearized partial data Calder\'on problem for Biharmonic operators

Author(s): Agrawal, Divyansh; Jaiswal, Ravi Shankar; Sahoo, Suman Kumar
Published in: 2023
Publisher: arXiv

Carleman estimates for geodesic X-ray transforms

Author(s): Gabriel P. Paternain, Mikko Salo
Published in: 2018
Publisher: arXiv

A minimization problem with free boundary and its application to inverse scattering problems

Author(s): Kow, Pu-Zhao; Salo, Mikko; Shahgholian, Henrik
Published in: 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2303.12605

The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform

Author(s): Shiqi Ma, Suman Kumar Sahoo, Mikko Salo
Published in: 2022
Publisher: arXiv

The non-Abelian X-ray transform on surfaces

Author(s): Gabriel P. Paternain, Mikko Salo
Published in: 2020
Publisher: arXiv

Unique continuation for the momentum ray transform

Author(s): Ilmavirta, Joonas; Kow, Pu-Zhao; Sahoo, Suman Kumar
Published in: 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2304.00327

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