Inverse boundary problems: toward a unified theory

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

Autores: Tuhin Ghosh, Angkana Rüland, Mikko Salo, Gunther Uhlmann
Publicado en: Journal of Functional Analysis, Edición 279/1, 2020, Página(s) 108505, ISSN 0022-1236
Editor: Academic Press
DOI: 10.1016/j.jfa.2020.108505

Jacobian of solutions to the conductivity equation in limited view

Autores: Mikko Salo; Hjørdis Schlüter
Publicado en: Inverse Problems, Edición Volume 39, Number 2, 2023, Página(s) 025001, ISSN 1361-6420
Editor: Institute of Physics
DOI: 10.1088/1361-6420/aca904

Fixed angle inverse scattering for sound speeds close to constant

Autores: Ma, Shiqi; Potenciano-Machado, Leyter; Salo, Mikko
Publicado en: SIAM Journal on Mathematical Analysis, Edición 55, 2023, ISSN 1095-7154
Editor: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m147640x

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

Autores: Mikko Salo, Leo Tzou
Publicado en: Proceedings of the American Mathematical Society, Edición Volume 151, 2023, Página(s) 2023-2030, ISSN 1088-6826
Editor: American Mathematical Society
DOI: 10.1090/proc/16255

Refined instability estimates for some inverse problems

Autores: Pu-Zhao Kow; Jenn-Nan Wang
Publicado en: Inverse Problems and Imaging, Edición 16, 2022, Página(s) 1619-1642, ISSN 1930-8337
Editor: American Institute of Mathematical Sciences
DOI: 10.3934/ipi.2022017

Inverse problems for a fractional conductivity equation

Autores: Giovanni Covi
Publicado en: Nonlinear Analysis, Edición 193, 2020, Página(s) 111418, ISSN 0362-546X
Editor: Pergamon Press Ltd.
DOI: 10.1016/j.na.2019.01.008

An inverse problem for semilinear equations involving the fractional Laplacian

Autores: Pu-Zhao Kow, Shiqi Ma, Suman Kumar Sahoo
Publicado en: Inverse Problems, Edición Volume 39, Number 9, 2023, Página(s) 095006, ISSN 1361-6420
Editor: Institute of Physics
DOI: 10.1088/1361-6420/ace9f4

On some partial data Calderón type problems with mixed boundary conditions

Autores: Giovanni Covi, Angkana Rüland
Publicado en: Journal of Differential Equations, Edición 288, 2021, Página(s) 141-203, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2021.04.004

The fixed angle scattering problem with a first order perturbation

Autores: Cristóbal J. Meroño, Leyter Potenciano-Machado, Mikko Salo
Publicado en: Annales Henri Poincaré, Edición 22, 2021, Página(s) 3699–3746, ISSN 1424-0637
Editor: Birkhauser Verlag
DOI: 10.1007/s00023-021-01081-w

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

Autores: Pu-Zhao Kow, Simon Larson, Mikko Salo, Henrik Shahgholian
Publicado en: Potential Analysis, 2023, ISSN 1572-929X
Editor: Springer
DOI: 10.1007/s11118-022-10054-5

The linearized Calderón problem for polyharmonic operators

Autores: Suman Kumar Sahoo, Mikko Salo
Publicado en: Journal of Differential Equations, Edición Volume 360, 2023, Página(s) 407-451, ISSN 1090-2732
Editor: Elsevier
DOI: 10.1016/j.jde.2023.03.017

Uniqueness in an inverse problem of fractional elasticity

Autores: Giovanni Covi, Maarten de Hoop, Mikko Salo
Publicado en: Proceedings of the Royal Society A, Edición Volume 479, issue 2278, 2023, Página(s) 20230474, ISSN 1471-2946
Editor: Royal Society
DOI: 10.1098/rspa.2023.0474

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

Autores: Krupchyk, Katya; Liimatainen, Tony; Salo, Mikko
Publicado en: Advances in Mathematics, Edición 402, 2022, Página(s) 108362, ISSN 0001-8708
Editor: Academic Press
DOI: 10.1016/j.aim.2022.108362

The Calderón problem for the fractional Schrödinger equation

Autores: Tuhin Ghosh; Mikko Salo; Gunther Uhlmann
Publicado en: Analysis & PDE, Edición Vol. 13, no. 2, 2020, Página(s) 455-475, ISSN 1948-206X
Editor: Mathematical Sciences Publishers
DOI: 10.2140/apde.2020.13.455

Inverse problems for elliptic equations with fractional power type nonlinearities

Autores: Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko; Tyni, Teemu
Publicado en: Journal of Differential Equations, Edición 306, 2021, Página(s) 189-219, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2021.10.015

Fixed angle inverse scattering in the presence of a Riemannian metric

Autores: Ma, Shiqi; Salo, Mikko
Publicado en: Journal of Inverse and Ill-posed Problems, Edición 30, 2021, Página(s) 495-520, ISSN 1569-3945
Editor: De Gruyter
DOI: 10.1515/jiip-2020-0119

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

Autores: Divyansh Agrawal; Venkateswaran P. Krishnan; Suman Kumar Sahoo
Publicado en: Journal of Geometric Analysis, Edición 32, 2022, Página(s) 245, ISSN 1050-6926
Editor: American Mathematical Society
DOI: 10.1007/s12220-022-00981-5

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

Autores: Giovanni Covi, Keijo Mönkkönen, Jesse Railo, Gunther Uhlmann
Publicado en: Advances in Mathematics, Edición 399, 2022, Página(s) 108246, ISSN 0001-8708
Editor: Academic Press
DOI: 10.1016/j.aim.2022.108246

Inverse problems for some fractional equations with general nonlinearity

Autores: Pu-Zhao Kow; Jenn-Nan Wang
Publicado en: Research in the Mathematical Sciences, Edición Volume 10, 2023, Página(s) 45, ISSN 2197-9847
Editor: Springer
DOI: 10.1007/s40687-023-00409-8

Free boundary methods and non-scattering phenomena

Autores: Mikko Salo; Henrik Shahgholian
Publicado en: Research in the Mathematical Sciences, Edición 13, 2021, ISSN 2522-0144
Editor: Springer
DOI: 10.48550/arxiv.2106.15154

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

Autores: Shuai Lu; Mikko Salo; Boxi Xu
Publicado en: Inverse Problems, Edición 38, 2022, Página(s) 065009, ISSN 0266-5611
Editor: Institute of Physics Publishing
DOI: 10.1088/1361-6420/ac637a

The Poisson embedding approach to the Calderón problem

Autores: Matti Lassas, Tony Liimatainen, Mikko Salo
Publicado en: Mathematische Annalen, Edición 377/1-2, 2020, Página(s) 19-67, ISSN 0025-5831
Editor: Springer Verlag
DOI: 10.1007/s00208-019-01818-3

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

Autores: Cristóbal J. Meroño, Leyter Potenciano-Machado, Mikko Salo
Publicado en: Revista Matemática Complutense, 2019, ISSN 1139-1138
Editor: Universidad Complutense de Madrid
DOI: 10.1007/s13163-019-00316-z

Dimension Bounds in Monotonicity Methods for the Helmholtz Equation

Autores: Bastian Harrach, Valter Pohjola, Mikko Salo
Publicado en: SIAM Journal on Mathematical Analysis, Edición 51/4, 2019, Página(s) 2995-3019, ISSN 0036-1410
Editor: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1240708

The Linearized Calderón Problem on Complex Manifolds

Autores: Colin Guillarmou, Mikko Salo, Leo Tzou
Publicado en: Acta Mathematica Sinica, English Series, Edición 35/6, 2019, Página(s) 1043-1056, ISSN 1439-8516
Editor: Springer Verlag
DOI: 10.1007/s10114-019-8129-7

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

Autores: R Rakesh, Mikko Salo
Publicado en: Inverse Problems, 2019, ISSN 0266-5611
Editor: Institute of Physics Publishing
DOI: 10.1088/1361-6420/ab23a2

Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations

Autores: Rakesh, Mikko Salo
Publicado en: SIAM Journal on Mathematical Analysis, Edición 52/6, 2020, Página(s) 5467-5499, ISSN 0036-1410
Editor: 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

Autores: Giovanni Covi, Keijo Mönkkönen, Jesse Railo
Publicado en: Inverse Problems and Imaging, Edición 15, 2021, Página(s) 641-681, ISSN 1930-8345
Editor: American Institute of Mathematical Sciences
DOI: 10.3934/ipi.2021009

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

Autores: Gabriel P. Paternain, Mikko Salo
Publicado en: Mathematische Zeitschrift, 2020, ISSN 0025-5874
Editor: Springer Verlag
DOI: 10.1007/s00209-020-02638-x

On Positivity Sets for Helmholtz Solutions

Autores: Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
Publicado en: Vietnam Journal of Mathematics, Edición Volume 51, 2023, Página(s) 985-994, ISSN 2305-2228
Editor: Springer
DOI: 10.1007/s10013-023-00646-y

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

Autores: Sombuddha Bhattacharyya; Venkateswaran P. Krishnan; Suman K. Sahoo
Publicado en: SIAM Journal on Mathematical Analysis, Edición Volume 55, Edición 4, 2023, ISSN 1095-7154
Editor: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1500617

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

Autores: Giovanni Covi
Publicado en: Inverse Problems, Edición 36/4, 2020, Página(s) 045004, ISSN 0266-5611
Editor: Institute of Physics Publishing
DOI: 10.1088/1361-6420/ab661a

Landis-type conjecture for the half-Laplacian

Autores: Pu-Zhao Kow, Jenn-Nan Wang
Publicado en: Proceedings of the American Mathematical Society, Edición Volume 151, 2023, Página(s) 2951-2962, ISSN 1088-6826
Editor: American Mathematical Society
DOI: 10.1090/proc/16093

On instability mechanisms for inverse problems

Autores: Herbert Koch, Angkana Rüland, Mikko Salo
Publicado en: Ars Inveniendi Analytica, Edición 7, 2021, ISSN 2769-8505
Editor: Ars Inveniendi
DOI: 10.15781/c93s-pk62

The fractional Calderón problem: Low regularity and stability

Autores: Angkana Rüland, Mikko Salo
Publicado en: Nonlinear Analysis, Edición 193, 2020, Página(s) 111529, ISSN 0362-546X
Editor: Pergamon Press Ltd.
DOI: 10.1016/j.na.2019.05.010

Applications of Microlocal Analysis in Inverse Problems

Autores: Mikko Salo
Publicado en: Mathematics, Edición 8/7, 2020, Página(s) 1184, ISSN 2227-7390
Editor: MDPI
DOI: 10.3390/math8071184

Limiting Carleman weights and conformally transversally anisotropic manifolds

Autores: Pablo Angulo, Daniel Faraco, Luis Guijarro, Mikko Salo
Publicado en: Transactions of the American Mathematical Society, Edición 373/7, 2020, Página(s) 5171-5197, ISSN 0002-9947
Editor: American Mathematical Society
DOI: 10.1090/tran/8072

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

Autores: Matti Lassas, Tony Liimatainen, Yi-Hsuan Lin, Mikko Salo
Publicado en: Revista Matemática Iberoamericana, Edición 37/4, 2021, Página(s) 1553-1580, ISSN 0213-2230
Editor: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1242

Inverse problems for elliptic equations with power type nonlinearities

Autores: Matti Lassas, Tony Liimatainen, Yi-Hsuan Lin, Mikko Salo
Publicado en: Journal de Mathématiques Pures et Appliquées, Edición 145, 2021, Página(s) 44-82, ISSN 0021-7824
Editor: Elsevier BV
DOI: 10.1016/j.matpur.2020.11.006

Geometric inverse problems

Autores: Gabriel P. Paternain; Mikko Salo; Gunther Uhlmann
Publicado en: Cambridge Studies in Advanced Mathematics, Edición 204, 2023, ISBN 9781009039901
Editor: Cambridge University Press
DOI: 10.1017/9781009039901

A general support theorem for analytic double fibration transforms

Autores: Mazzucchelli, Marco; Salo, Mikko; Tzou, Leo
Publicado en: 2023
Editor: arXiv
DOI: 10.48550/arxiv.2306.05906

Inverse problems for real principal type operators

Autores: Oksanen, Lauri; Salo, Mikko; Stefanov, Plamen; Uhlmann, Gunther
Publicado en: 2020
Editor: arXiv

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

Autores: Bhattacharyya, Sombuddha; Krishnan, Venkateswaran P.; Sahoo, Suman Kumar
Publicado en: 2021
Editor: arXiv
DOI: 10.48550/arxiv.2111.07610

On scattering behavior of corner domains with anisotropic inhomogeneities

Autores: Kow, Pu-Zhao; Salo, Mikko; Shahgholian, Henrik
Publicado en: 2023
Editor: arXiv
DOI: 10.48550/arxiv.2309.11213

Linearized partial data Calder\'on problem for Biharmonic operators

Autores: Agrawal, Divyansh; Jaiswal, Ravi Shankar; Sahoo, Suman Kumar
Publicado en: 2023
Editor: arXiv

Carleman estimates for geodesic X-ray transforms

Autores: Gabriel P. Paternain, Mikko Salo
Publicado en: 2018
Editor: arXiv

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

Autores: Kow, Pu-Zhao; Salo, Mikko; Shahgholian, Henrik
Publicado en: 2023
Editor: arXiv
DOI: 10.48550/arxiv.2303.12605

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

Autores: Shiqi Ma, Suman Kumar Sahoo, Mikko Salo
Publicado en: 2022
Editor: arXiv

The non-Abelian X-ray transform on surfaces

Autores: Gabriel P. Paternain, Mikko Salo
Publicado en: 2020
Editor: arXiv

Unique continuation for the momentum ray transform

Autores: Ilmavirta, Joonas; Kow, Pu-Zhao; Sahoo, Suman Kumar
Publicado en: 2023
Editor: arXiv
DOI: 10.48550/arxiv.2304.00327

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