Inverse boundary problems: toward a unified theory

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

Autorzy: Tuhin Ghosh, Angkana Rüland, Mikko Salo, Gunther Uhlmann
Opublikowane w: Journal of Functional Analysis, Numer 279/1, 2020, Strona(/y) 108505, ISSN 0022-1236
Wydawca: Academic Press
DOI: 10.1016/j.jfa.2020.108505

Jacobian of solutions to the conductivity equation in limited view

Autorzy: Mikko Salo; Hjørdis Schlüter
Opublikowane w: Inverse Problems, Numer Volume 39, Number 2, 2023, Strona(/y) 025001, ISSN 1361-6420
Wydawca: Institute of Physics
DOI: 10.1088/1361-6420/aca904

Fixed angle inverse scattering for sound speeds close to constant

Autorzy: Ma, Shiqi; Potenciano-Machado, Leyter; Salo, Mikko
Opublikowane w: SIAM Journal on Mathematical Analysis, Numer 55, 2023, ISSN 1095-7154
Wydawca: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m147640x

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

Autorzy: Mikko Salo, Leo Tzou
Opublikowane w: Proceedings of the American Mathematical Society, Numer Volume 151, 2023, Strona(/y) 2023-2030, ISSN 1088-6826
Wydawca: American Mathematical Society
DOI: 10.1090/proc/16255

Refined instability estimates for some inverse problems

Autorzy: Pu-Zhao Kow; Jenn-Nan Wang
Opublikowane w: Inverse Problems and Imaging, Numer 16, 2022, Strona(/y) 1619-1642, ISSN 1930-8337
Wydawca: American Institute of Mathematical Sciences
DOI: 10.3934/ipi.2022017

Inverse problems for a fractional conductivity equation

Autorzy: Giovanni Covi
Opublikowane w: Nonlinear Analysis, Numer 193, 2020, Strona(/y) 111418, ISSN 0362-546X
Wydawca: Pergamon Press Ltd.
DOI: 10.1016/j.na.2019.01.008

An inverse problem for semilinear equations involving the fractional Laplacian

Autorzy: Pu-Zhao Kow, Shiqi Ma, Suman Kumar Sahoo
Opublikowane w: Inverse Problems, Numer Volume 39, Number 9, 2023, Strona(/y) 095006, ISSN 1361-6420
Wydawca: Institute of Physics
DOI: 10.1088/1361-6420/ace9f4

On some partial data Calderón type problems with mixed boundary conditions

Autorzy: Giovanni Covi, Angkana Rüland
Opublikowane w: Journal of Differential Equations, Numer 288, 2021, Strona(/y) 141-203, ISSN 0022-0396
Wydawca: Academic Press
DOI: 10.1016/j.jde.2021.04.004

The fixed angle scattering problem with a first order perturbation

Autorzy: Cristóbal J. Meroño, Leyter Potenciano-Machado, Mikko Salo
Opublikowane w: Annales Henri Poincaré, Numer 22, 2021, Strona(/y) 3699–3746, ISSN 1424-0637
Wydawca: Birkhauser Verlag
DOI: 10.1007/s00023-021-01081-w

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

Autorzy: Pu-Zhao Kow, Simon Larson, Mikko Salo, Henrik Shahgholian
Opublikowane w: Potential Analysis, 2023, ISSN 1572-929X
Wydawca: Springer
DOI: 10.1007/s11118-022-10054-5

The linearized Calderón problem for polyharmonic operators

Autorzy: Suman Kumar Sahoo, Mikko Salo
Opublikowane w: Journal of Differential Equations, Numer Volume 360, 2023, Strona(/y) 407-451, ISSN 1090-2732
Wydawca: Elsevier
DOI: 10.1016/j.jde.2023.03.017

Uniqueness in an inverse problem of fractional elasticity

Autorzy: Giovanni Covi, Maarten de Hoop, Mikko Salo
Opublikowane w: Proceedings of the Royal Society A, Numer Volume 479, issue 2278, 2023, Strona(/y) 20230474, ISSN 1471-2946
Wydawca: Royal Society
DOI: 10.1098/rspa.2023.0474

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

Autorzy: Krupchyk, Katya; Liimatainen, Tony; Salo, Mikko
Opublikowane w: Advances in Mathematics, Numer 402, 2022, Strona(/y) 108362, ISSN 0001-8708
Wydawca: Academic Press
DOI: 10.1016/j.aim.2022.108362

The Calderón problem for the fractional Schrödinger equation

Autorzy: Tuhin Ghosh; Mikko Salo; Gunther Uhlmann
Opublikowane w: Analysis & PDE, Numer Vol. 13, no. 2, 2020, Strona(/y) 455-475, ISSN 1948-206X
Wydawca: Mathematical Sciences Publishers
DOI: 10.2140/apde.2020.13.455

Inverse problems for elliptic equations with fractional power type nonlinearities

Autorzy: Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko; Tyni, Teemu
Opublikowane w: Journal of Differential Equations, Numer 306, 2021, Strona(/y) 189-219, ISSN 0022-0396
Wydawca: Academic Press
DOI: 10.1016/j.jde.2021.10.015

Fixed angle inverse scattering in the presence of a Riemannian metric

Autorzy: Ma, Shiqi; Salo, Mikko
Opublikowane w: Journal of Inverse and Ill-posed Problems, Numer 30, 2021, Strona(/y) 495-520, ISSN 1569-3945
Wydawca: De Gruyter
DOI: 10.1515/jiip-2020-0119

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

Autorzy: Divyansh Agrawal; Venkateswaran P. Krishnan; Suman Kumar Sahoo
Opublikowane w: Journal of Geometric Analysis, Numer 32, 2022, Strona(/y) 245, ISSN 1050-6926
Wydawca: American Mathematical Society
DOI: 10.1007/s12220-022-00981-5

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

Autorzy: Giovanni Covi, Keijo Mönkkönen, Jesse Railo, Gunther Uhlmann
Opublikowane w: Advances in Mathematics, Numer 399, 2022, Strona(/y) 108246, ISSN 0001-8708
Wydawca: Academic Press
DOI: 10.1016/j.aim.2022.108246

Inverse problems for some fractional equations with general nonlinearity

Autorzy: Pu-Zhao Kow; Jenn-Nan Wang
Opublikowane w: Research in the Mathematical Sciences, Numer Volume 10, 2023, Strona(/y) 45, ISSN 2197-9847
Wydawca: Springer
DOI: 10.1007/s40687-023-00409-8

Free boundary methods and non-scattering phenomena

Autorzy: Mikko Salo; Henrik Shahgholian
Opublikowane w: Research in the Mathematical Sciences, Numer 13, 2021, ISSN 2522-0144
Wydawca: Springer
DOI: 10.48550/arxiv.2106.15154

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

Autorzy: Shuai Lu; Mikko Salo; Boxi Xu
Opublikowane w: Inverse Problems, Numer 38, 2022, Strona(/y) 065009, ISSN 0266-5611
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6420/ac637a

The Poisson embedding approach to the Calderón problem

Autorzy: Matti Lassas, Tony Liimatainen, Mikko Salo
Opublikowane w: Mathematische Annalen, Numer 377/1-2, 2020, Strona(/y) 19-67, ISSN 0025-5831
Wydawca: Springer Verlag
DOI: 10.1007/s00208-019-01818-3

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

Autorzy: Cristóbal J. Meroño, Leyter Potenciano-Machado, Mikko Salo
Opublikowane w: Revista Matemática Complutense, 2019, ISSN 1139-1138
Wydawca: Universidad Complutense de Madrid
DOI: 10.1007/s13163-019-00316-z

Dimension Bounds in Monotonicity Methods for the Helmholtz Equation

Autorzy: Bastian Harrach, Valter Pohjola, Mikko Salo
Opublikowane w: SIAM Journal on Mathematical Analysis, Numer 51/4, 2019, Strona(/y) 2995-3019, ISSN 0036-1410
Wydawca: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1240708

The Linearized Calderón Problem on Complex Manifolds

Autorzy: Colin Guillarmou, Mikko Salo, Leo Tzou
Opublikowane w: Acta Mathematica Sinica, English Series, Numer 35/6, 2019, Strona(/y) 1043-1056, ISSN 1439-8516
Wydawca: Springer Verlag
DOI: 10.1007/s10114-019-8129-7

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

Autorzy: R Rakesh, Mikko Salo
Opublikowane w: Inverse Problems, 2019, ISSN 0266-5611
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6420/ab23a2

Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations

Autorzy: Rakesh, Mikko Salo
Opublikowane w: SIAM Journal on Mathematical Analysis, Numer 52/6, 2020, Strona(/y) 5467-5499, ISSN 0036-1410
Wydawca: 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

Autorzy: Giovanni Covi, Keijo Mönkkönen, Jesse Railo
Opublikowane w: Inverse Problems and Imaging, Numer 15, 2021, Strona(/y) 641-681, ISSN 1930-8345
Wydawca: American Institute of Mathematical Sciences
DOI: 10.3934/ipi.2021009

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

Autorzy: Gabriel P. Paternain, Mikko Salo
Opublikowane w: Mathematische Zeitschrift, 2020, ISSN 0025-5874
Wydawca: Springer Verlag
DOI: 10.1007/s00209-020-02638-x

On Positivity Sets for Helmholtz Solutions

Autorzy: Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
Opublikowane w: Vietnam Journal of Mathematics, Numer Volume 51, 2023, Strona(/y) 985-994, ISSN 2305-2228
Wydawca: Springer
DOI: 10.1007/s10013-023-00646-y

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

Autorzy: Sombuddha Bhattacharyya; Venkateswaran P. Krishnan; Suman K. Sahoo
Opublikowane w: SIAM Journal on Mathematical Analysis, Numer Volume 55, Numer 4, 2023, ISSN 1095-7154
Wydawca: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1500617

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

Autorzy: Giovanni Covi
Opublikowane w: Inverse Problems, Numer 36/4, 2020, Strona(/y) 045004, ISSN 0266-5611
Wydawca: Institute of Physics Publishing
DOI: 10.1088/1361-6420/ab661a

Landis-type conjecture for the half-Laplacian

Autorzy: Pu-Zhao Kow, Jenn-Nan Wang
Opublikowane w: Proceedings of the American Mathematical Society, Numer Volume 151, 2023, Strona(/y) 2951-2962, ISSN 1088-6826
Wydawca: American Mathematical Society
DOI: 10.1090/proc/16093

On instability mechanisms for inverse problems

Autorzy: Herbert Koch, Angkana Rüland, Mikko Salo
Opublikowane w: Ars Inveniendi Analytica, Numer 7, 2021, ISSN 2769-8505
Wydawca: Ars Inveniendi
DOI: 10.15781/c93s-pk62

The fractional Calderón problem: Low regularity and stability

Autorzy: Angkana Rüland, Mikko Salo
Opublikowane w: Nonlinear Analysis, Numer 193, 2020, Strona(/y) 111529, ISSN 0362-546X
Wydawca: Pergamon Press Ltd.
DOI: 10.1016/j.na.2019.05.010

Applications of Microlocal Analysis in Inverse Problems

Autorzy: Mikko Salo
Opublikowane w: Mathematics, Numer 8/7, 2020, Strona(/y) 1184, ISSN 2227-7390
Wydawca: MDPI
DOI: 10.3390/math8071184

Limiting Carleman weights and conformally transversally anisotropic manifolds

Autorzy: Pablo Angulo, Daniel Faraco, Luis Guijarro, Mikko Salo
Opublikowane w: Transactions of the American Mathematical Society, Numer 373/7, 2020, Strona(/y) 5171-5197, ISSN 0002-9947
Wydawca: American Mathematical Society
DOI: 10.1090/tran/8072

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

Autorzy: Matti Lassas, Tony Liimatainen, Yi-Hsuan Lin, Mikko Salo
Opublikowane w: Revista Matemática Iberoamericana, Numer 37/4, 2021, Strona(/y) 1553-1580, ISSN 0213-2230
Wydawca: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1242

Inverse problems for elliptic equations with power type nonlinearities

Autorzy: Matti Lassas, Tony Liimatainen, Yi-Hsuan Lin, Mikko Salo
Opublikowane w: Journal de Mathématiques Pures et Appliquées, Numer 145, 2021, Strona(/y) 44-82, ISSN 0021-7824
Wydawca: Elsevier BV
DOI: 10.1016/j.matpur.2020.11.006

Geometric inverse problems

Autorzy: Gabriel P. Paternain; Mikko Salo; Gunther Uhlmann
Opublikowane w: Cambridge Studies in Advanced Mathematics, Numer 204, 2023, ISBN 9781009039901
Wydawca: Cambridge University Press
DOI: 10.1017/9781009039901

A general support theorem for analytic double fibration transforms

Autorzy: Mazzucchelli, Marco; Salo, Mikko; Tzou, Leo
Opublikowane w: 2023
Wydawca: arXiv
DOI: 10.48550/arxiv.2306.05906

Inverse problems for real principal type operators

Autorzy: Oksanen, Lauri; Salo, Mikko; Stefanov, Plamen; Uhlmann, Gunther
Opublikowane w: 2020
Wydawca: arXiv

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

Autorzy: Bhattacharyya, Sombuddha; Krishnan, Venkateswaran P.; Sahoo, Suman Kumar
Opublikowane w: 2021
Wydawca: arXiv
DOI: 10.48550/arxiv.2111.07610

On scattering behavior of corner domains with anisotropic inhomogeneities

Autorzy: Kow, Pu-Zhao; Salo, Mikko; Shahgholian, Henrik
Opublikowane w: 2023
Wydawca: arXiv
DOI: 10.48550/arxiv.2309.11213

Linearized partial data Calder\'on problem for Biharmonic operators

Autorzy: Agrawal, Divyansh; Jaiswal, Ravi Shankar; Sahoo, Suman Kumar
Opublikowane w: 2023
Wydawca: arXiv

Carleman estimates for geodesic X-ray transforms

Autorzy: Gabriel P. Paternain, Mikko Salo
Opublikowane w: 2018
Wydawca: arXiv

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

Autorzy: Kow, Pu-Zhao; Salo, Mikko; Shahgholian, Henrik
Opublikowane w: 2023
Wydawca: arXiv
DOI: 10.48550/arxiv.2303.12605

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

Autorzy: Shiqi Ma, Suman Kumar Sahoo, Mikko Salo
Opublikowane w: 2022
Wydawca: arXiv

The non-Abelian X-ray transform on surfaces

Autorzy: Gabriel P. Paternain, Mikko Salo
Opublikowane w: 2020
Wydawca: arXiv

Unique continuation for the momentum ray transform

Autorzy: Ilmavirta, Joonas; Kow, Pu-Zhao; Sahoo, Suman Kumar
Opublikowane w: 2023
Wydawca: arXiv
DOI: 10.48550/arxiv.2304.00327

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