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Journal articles on the topic 'Calderon problem'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Arridge, Simon, Shari Moskow, and John C. Schotland. "Inverse Born series for the Calderon problem." Inverse Problems 28, no. 3 (2012): 035003. http://dx.doi.org/10.1088/0266-5611/28/3/035003.

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2

Andrieux, S., and H. D. Bui. "On some nonlinear inverse problems in elasticity." Theoretical and Applied Mechanics 38, no. 2 (2011): 125–54. http://dx.doi.org/10.2298/tam1102125a.

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In this paper, we make a review of some inverse problems in elasticity, in statics and dynamics, in acoustics, thermoelasticity and viscoelasticity. Crack inverse problems have been solved in closed form, by considering a nonlinear variational equation provided by the reciprocity gap functional. This equation involves the unknown geometry of the crack and the boundary data. It results from the symmetry lost between current fields and adjoint fields which is related to their support. The nonlinear equation is solved step by step by considering linear inverse problems. The normal to the crack pl

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3

Novikov, R. G. "New global stability estimates for the Gel'fand–Calderon inverse problem." Inverse Problems 27, no. 1 (2010): 015001. http://dx.doi.org/10.1088/0266-5611/27/1/015001.

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4

Ortiz G., John E., Axelle Pillain, Lyes Rahmouni, and Francesco P. Andriulli. "A Calderon regularized symmetric formulation for the electroencephalography forward problem." Journal of Computational Physics 375 (December 2018): 291–306. http://dx.doi.org/10.1016/j.jcp.2018.07.048.

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5

Belishev, M. I. "The Calderon Problem for Two-Dimensional Manifolds by the BC-Method." SIAM Journal on Mathematical Analysis 35, no. 1 (2003): 172–82. http://dx.doi.org/10.1137/s0036141002413919.

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6

Runovski, K., and H. J. Schmeisser. "Inequalities of Calderon–Zygmund Type for Trigonometric Polynomials." gmj 8, no. 1 (2001): 165–79. http://dx.doi.org/10.1515/gmj.2001.165.

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Abstract We give a unified approach to inequalities of Calderon–Zygmund type for trigonometric polynomials of several variables based on the Fourier analytic methods. Sharp results are achieved for the full range of admissible parameters p, 0 < p ≤ +∞. The results obtained are applied to the problem of the image of the Fourier transform in the scale of Besov spaces.

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7

Gadjiev, Tahir S., Vagif S. Guliyev, and Konul G. Suleymanova. "The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces." Studia Scientiarum Mathematicarum Hungarica 57, no. 1 (2020): 68–90. http://dx.doi.org/10.1556/012.2020.57.1.1449.

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Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

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8

Faraco, D., and K. M. Rogers. "THE SOBOLEV NORM OF CHARACTERISTIC FUNCTIONS WITH APPLICATIONS TO THE CALDERON INVERSE PROBLEM." Quarterly Journal of Mathematics 64, no. 1 (2012): 133–47. http://dx.doi.org/10.1093/qmath/har039.

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9

Savchuk, A. M. "The Calderon-Zygmund Operator and Its Relation to Asymptotic Estimates for Ordinary Diﬀerential Operators". Contemporary Mathematics. Fundamental Directions 63, № 4 (2017): 689–702. http://dx.doi.org/10.22363/2413-3639-2017-63-4-689-702.

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We consider the problem of estimating of expressions of the kind Υ(λ)=supx∈[0,1]∣∣∫x0f(t)eiλtdt∣∣. In particular, for the case f∈Lp[0,1], p∈(1,2], we prove the estimate ∥Υ(λ)∥Lq(R)≤C∥f∥Lp for any q>p′, where 1/p+1/p′=1. The same estimate is proved for the space Lq(dμ), where dμ is an arbitrary Carleson measure in the upper half-plane C+. Also, we estimate more complex expressions of the kind Υ(λ) arising in study of asymptotics of the fundamental system of solutions for systems of the kind y′=By+A(x)y+C(x,λ)y with dimension n as |λ|→∞ in suitable sectors of the complex plane.

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10

Strand, Carolyn A., Sandra T. Welch, Sarah A. Holmes, and Steven L. Judd. "Developing Student Abilities to Recognize Risk Factors: A Series of Scenarios." Issues in Accounting Education 17, no. 1 (2002): 57–67. http://dx.doi.org/10.2308/iace.2002.17.1.57.

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Misappropriation of assets is an expensive and growing problem. However, detecting this type of fraud is very difficult. Green and Calderon (1996) claim that externally observable risk factors can help signal the likelihood of fraud. Awareness and timely recognition of these “red flags” might improve an individual's ability to assess the potential vulnerability of an organization to fraud. Contained herein is a case consisting of five scenarios that deal with the risk factors identified in Statement on Auditing Standards (SAS) No. 82, Consideration of Fraud in a Financial Statement Audit (AICP

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11

Marter, Joan M. "The Engineer Behind Calder’s Art." Mechanical Engineering 120, no. 12 (1998): 53–57. http://dx.doi.org/10.1115/1.1998-dec-2.

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This article reviews the significance of Alexander Calder’s, a renowned sculptor, technical and engineering expertise that has become increasingly clear in recent years. Calder’s most important innovation in the development of wire sculpture was the suspension of his wire forms from a single wire thread. A small wood-and-wire caricature of a monkey was the first, soon followed by several caricatures of Josephine Baker, the star of La Revue N è gre at the Folies Bergè re and an international sensation in 1925. Like Leonardo da Vinci, Calder was primarily interested in problem solving, in experi

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12

Cekić, Mihajlo. "Calderón problem for connections." Communications in Partial Differential Equations 42, no. 11 (2017): 1781–836. http://dx.doi.org/10.1080/03605302.2017.1390678.

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13

Abraham, Kweku, and Richard Nickl. "On statistical Calderón problems." Mathematical Statistics and Learning 2, no. 2 (2020): 165–216. http://dx.doi.org/10.4171/msl/14.

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14

Cekić, Mihajlo. "Calderón problem for Yang–Mills connections." Journal of Spectral Theory 10, no. 2 (2020): 463–513. http://dx.doi.org/10.4171/jst/302.

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15

Kenig, Carlos, and Gunther Uhlmann. "The Calderón problem with partial data." Annals of Mathematics 165, no. 2 (2007): 567–91. http://dx.doi.org/10.4007/annals.2007.165.567.

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16

Ferreira, David Dos Santos, Carlos E. Kenig, Johannes Sjöstrand, and Gunther Uhlmann. "On the linearized local Calderón problem." Mathematical Research Letters 16, no. 6 (2009): 955–70. http://dx.doi.org/10.4310/mrl.2009.v16.n6.a4.

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17

Piiroinen, Petteri, and Martin Simon. "Probabilistic interpretation of the Calderón problem." Inverse Problems & Imaging 11, no. 3 (2017): 553–75. http://dx.doi.org/10.3934/ipi.2017026.

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18

Caro, Pedro, and Andoni Garcia. "The Calderón problem with corrupted data." Inverse Problems 33, no. 8 (2017): 085001. http://dx.doi.org/10.1088/1361-6420/aa7425.

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19

Ameur, Yacin. "The Calderón problem for Hilbert couples." Arkiv för Matematik 41, no. 2 (2003): 203–31. http://dx.doi.org/10.1007/bf02390812.

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20

Munnier, Alexandre, and Karim Ramdani. "Calderón cavities inverse problem as a shape-from-moments problem." Quarterly of Applied Mathematics 76, no. 3 (2018): 407–35. http://dx.doi.org/10.1090/qam/1505.

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21

Dos Santos Ferreira, David, Yaroslav Kurylev, Matti Lassas, and Mikko Salo. "The Calderón problem in transversally anisotropic geometries." Journal of the European Mathematical Society 18, no. 11 (2016): 2579–626. http://dx.doi.org/10.4171/jems/649.

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22

Rüland, Angkana, and Mikko Salo. "Exponential instability in the fractional Calderón problem." Inverse Problems 34, no. 4 (2018): 045003. http://dx.doi.org/10.1088/1361-6420/aaac5a.

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23

Guillarmou, Colin, Mikko Salo, and Leo Tzou. "The Linearized Calderón Problem on Complex Manifolds." Acta Mathematica Sinica, English Series 35, no. 6 (2019): 1043–56. http://dx.doi.org/10.1007/s10114-019-8129-7.

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24

Muñoz, Claudio, and Gunther Uhlmann. "The Calderón problem for quasilinear elliptic equations." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 37, no. 5 (2020): 1143–66. http://dx.doi.org/10.1016/j.anihpc.2020.03.004.

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25

Santacesaria, Matteo. "New global stability estimates for the Calderón problem in two dimensions." Journal of the Institute of Mathematics of Jussieu 12, no. 3 (2012): 553–69. http://dx.doi.org/10.1017/s147474801200076x.

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AbstractWe prove a new global stability estimate for the Gel’fand–Calderón inverse problem on a two-dimensional bounded domain. Specifically, the inverse boundary value problem for the equation ${- }\Delta \psi + v\hspace{0.167em} \psi = 0$ on $D$ is analysed, where $v$ is a smooth real-valued potential of conductivity type defined on a bounded planar domain $D$. The main feature of this estimate is that it shows that the smoother a potential is, the more stable its reconstruction is. Furthermore, the stability is proven to depend exponentially on the smoothness, in a sense to be made precise.

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26

Sjöstrand, Johannes, and Gunther Uhlmann. "Local analytic regularity in the linearized Calderón problem." Analysis & PDE 9, no. 3 (2016): 515–44. http://dx.doi.org/10.2140/apde.2016.9.515.

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27

Ghosh, Tuhin, Mikko Salo, and Gunther Uhlmann. "The Calderón problem for the fractional Schrödinger equation." Analysis & PDE 13, no. 2 (2020): 455–75. http://dx.doi.org/10.2140/apde.2020.13.455.

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28

Rüland, Angkana, and Mikko Salo. "The fractional Calderón problem: Low regularity and stability." Nonlinear Analysis 193 (April 2020): 111529. http://dx.doi.org/10.1016/j.na.2019.05.010.

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29

Nachman, Adrian, and Brian Street. "Reconstruction in the Calderón Problem with Partial Data." Communications in Partial Differential Equations 35, no. 2 (2010): 375–90. http://dx.doi.org/10.1080/03605300903296322.

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30

Yu. Imanuvilov, Oleg, and Masahiro Yamamoto. "Calderón problem for Maxwell's equations in cylindrical domain." Inverse Problems & Imaging 8, no. 4 (2014): 1117–37. http://dx.doi.org/10.3934/ipi.2014.8.1117.

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31

Caro, Pedro, and Mikko Salo. "Stability of the Calderón problem in admissible geometries." Inverse Problems & Imaging 8, no. 4 (2014): 939–57. http://dx.doi.org/10.3934/ipi.2014.8.939.

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32

Faierman, M. "The Calderón approach to an elliptic boundary problem." Mathematische Nachrichten 282, no. 8 (2009): 1134–58. http://dx.doi.org/10.1002/mana.200610792.

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33

Li, Li. "The Calderón problem for the fractional magnetic operator." Inverse Problems 36, no. 7 (2020): 075003. http://dx.doi.org/10.1088/1361-6420/ab8445.

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34

Lassas, Matti, Tony Liimatainen, and Mikko Salo. "The Poisson embedding approach to the Calderón problem." Mathematische Annalen 377, no. 1-2 (2019): 19–67. http://dx.doi.org/10.1007/s00208-019-01818-3.

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35

Cârstea, Cătălin I., Ali Feizmohammadi, Yavar Kian, Katya Krupchyk, and Gunther Uhlmann. "The Calderón inverse problem for isotropic quasilinear conductivities." Advances in Mathematics 391 (November 2021): 107956. http://dx.doi.org/10.1016/j.aim.2021.107956.

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36

Mingione, Giuseppe. "Calderón–Zygmund estimates for measure data problems." Comptes Rendus Mathematique 344, no. 7 (2007): 437–42. http://dx.doi.org/10.1016/j.crma.2007.02.005.

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37

Byun, Sun-Sig, and Jehan Oh. "Global gradient estimates for asymptotically regular problems of p(x)-Laplacian type." Communications in Contemporary Mathematics 20, no. 08 (2018): 1750079. http://dx.doi.org/10.1142/s0219199717500791.

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We study an asymptotically regular problem of [Formula: see text]-Laplacian type with discontinuous nonlinearity in a nonsmooth bounded domain. A global Calderón–Zygmund estimate is established for such a nonlinear elliptic problem with nonstandard growth under the assumption that the associated nonlinearity has a more general kind of the asymptotic behavior near the infinity with respect to the gradient variable. We also address an optimal regularity requirement on the nonlinearity as well as a minimal geometric assumption on the boundary of the domain for the nonlinear Calderón–Zygmund theor

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38

Lassas, Matti, Mikko Salo, and Leo Tzou. "Inverse problems and invisibility cloaking for FEM models and resistor networks." Mathematical Models and Methods in Applied Sciences 25, no. 02 (2014): 309–42. http://dx.doi.org/10.1142/s0218202515500116.

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In this paper we consider inverse problems for resistor networks and for models obtained via the finite element method (FEM) for the conductivity equation. These correspond to discrete versions of the inverse conductivity problem of Calderón. We characterize FEM models corresponding to a given triangulation of the domain that are equivalent to certain resistor networks, and apply the results to study nonuniqueness of the discrete inverse problem. It turns out that the degree of nonuniqueness for the discrete problem is larger than the one for the partial differential equation. We also study in

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39

Rüland, Angkana, and Mikko Salo. "Quantitative Runge Approximation and Inverse Problems." International Mathematics Research Notices 2019, no. 20 (2018): 6216–34. http://dx.doi.org/10.1093/imrn/rnx301.

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AbstractIn this short note, we provide a quantitative version of the classical Runge approximation property for second-order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We show that these estimates are essentially optimal. As a model application, we provide a new proof of the result from [8], [2] on stability for the Calderón problem with local data.

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40

Imanuvilov, Oleg Yu, Gunther Uhlmann, and Masahiro Yamamoto. "The Calderón problem with partial data in two dimensions." Journal of the American Mathematical Society 23, no. 3 (2010): 655. http://dx.doi.org/10.1090/s0894-0347-10-00656-9.

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41

Behrndt, Jussi, and Jonathan Rohleder. "An Inverse Problem of Calderón Type with Partial Data." Communications in Partial Differential Equations 37, no. 6 (2012): 1141–59. http://dx.doi.org/10.1080/03605302.2011.632464.

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42

Ghosh, Tuhin, Yi-Hsuan Lin, and Jingni Xiao. "The Calderón problem for variable coefficients nonlocal elliptic operators." Communications in Partial Differential Equations 42, no. 12 (2017): 1923–61. http://dx.doi.org/10.1080/03605302.2017.1390681.

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43

Barceló, Tomeu, Daniel Faraco, and Alberto Ruiz. "Stability of Calderón inverse conductivity problem in the plane." Journal de Mathématiques Pures et Appliquées 88, no. 6 (2007): 522–56. http://dx.doi.org/10.1016/j.matpur.2007.07.006.

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44

Guillarmou, Colin, and Leo Tzou. "Calderón inverse problem with partial data on Riemann surfaces." Duke Mathematical Journal 158, no. 1 (2011): 83–120. http://dx.doi.org/10.1215/00127094-1276310.

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45

Caro, Pedro, Andoni García, and Juan Manuel Reyes. "Stability of the Calderón problem for less regular conductivities." Journal of Differential Equations 254, no. 2 (2013): 469–92. http://dx.doi.org/10.1016/j.jde.2012.08.018.

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46

Caro, Pedro, David Dos Santos Ferreira, and Alberto Ruiz. "Stability estimates for the Calderón problem with partial data." Journal of Differential Equations 260, no. 3 (2016): 2457–89. http://dx.doi.org/10.1016/j.jde.2015.10.007.

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47

Ham, Seheon, Yehyun Kwon, and Sanghyuk Lee. "Uniqueness in the Calderón problem and bilinear restriction estimates." Journal of Functional Analysis 281, no. 8 (2021): 109119. http://dx.doi.org/10.1016/j.jfa.2021.109119.

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48

Rüland, Angkana. "On Single Measurement Stability for the Fractional Calderón Problem." SIAM Journal on Mathematical Analysis 53, no. 5 (2021): 5094–113. http://dx.doi.org/10.1137/20m1381964.

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49

Ervedoza, S., and F. de Gournay. "Uniform stability estimates for the discrete Calderón problems." Inverse Problems 27, no. 12 (2011): 125012. http://dx.doi.org/10.1088/0266-5611/27/12/125012.

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50

Baasandorj, Sumiya, Sun-Sig Byun, and Jehan Oh. "Calderón-Zygmund estimates for generalized double phase problems." Journal of Functional Analysis 279, no. 7 (2020): 108670. http://dx.doi.org/10.1016/j.jfa.2020.108670.

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