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Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations
1. | Faculty of Mathematics, Al.I.Cuza University, Iasi, 700506, Romania |
2. | Institute of Mathematics, Helsinki University of Technology, P.O.Box 1100, 02015 Helsinki, Finland |
[1] |
Carlos Durán, Diego Otero. The projective Cartan-Klein geometry of the Helmholtz conditions. Journal of Geometric Mechanics, 2018, 10 (1) : 69-92. doi: 10.3934/jgm.2018003 |
[2] |
J. C. Alvarez Paiva and E. Fernandes. Crofton formulas in projective Finsler spaces. Electronic Research Announcements, 1998, 4: 91-100. |
[3] |
Michael V. Klibanov. A phaseless inverse scattering problem for the 3-D Helmholtz equation. Inverse Problems and Imaging, 2017, 11 (2) : 263-276. doi: 10.3934/ipi.2017013 |
[4] |
Karzan Berdawood, Abdeljalil Nachaoui, Rostam Saeed, Mourad Nachaoui, Fatima Aboud. An efficient D-N alternating algorithm for solving an inverse problem for Helmholtz equation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : 57-78. doi: 10.3934/dcdss.2021013 |
[5] |
Giulio Ciraolo, Antonio Greco. An overdetermined problem associated to the Finsler Laplacian. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1025-1038. doi: 10.3934/cpaa.2021004 |
[6] |
Kien Trung Nguyen, Vo Nguyen Minh Hieu, Van Huy Pham. Inverse group 1-median problem on trees. Journal of Industrial and Management Optimization, 2021, 17 (1) : 221-232. doi: 10.3934/jimo.2019108 |
[7] |
Hui Liu, Yiming Long, Yuming Xiao. The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3803-3829. doi: 10.3934/dcds.2018165 |
[8] |
Jesús Carrillo-Pacheco, Felipe Zaldivar. On codes over FFN$(1,q)$-projective varieties. Advances in Mathematics of Communications, 2016, 10 (2) : 209-220. doi: 10.3934/amc.2016001 |
[9] |
Antonio Giorgilli, Stefano Marmi. Convergence radius in the Poincaré-Siegel problem. Discrete and Continuous Dynamical Systems - S, 2010, 3 (4) : 601-621. doi: 10.3934/dcdss.2010.3.601 |
[10] |
Jussi Korpela, Matti Lassas, Lauri Oksanen. Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation. Inverse Problems and Imaging, 2019, 13 (3) : 575-596. doi: 10.3934/ipi.2019027 |
[11] |
Carlos Durán, Diego Otero. The projective symplectic geometry of higher order variational problems: Minimality conditions. Journal of Geometric Mechanics, 2016, 8 (3) : 305-322. doi: 10.3934/jgm.2016009 |
[12] |
Lidan Li, Hongwei Zhang, Liwei Zhang. Inverse quadratic programming problem with $ l_1 $ norm measure. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2425-2437. doi: 10.3934/jimo.2019061 |
[13] |
Alexey Smirnov, Michael Klibanov, Loc Nguyen. Convexification for a 1D hyperbolic coefficient inverse problem with single measurement data. Inverse Problems and Imaging, 2020, 14 (5) : 913-938. doi: 10.3934/ipi.2020042 |
[14] |
Michael V. Klibanov, Loc H. Nguyen, Anders Sullivan, Lam Nguyen. A globally convergent numerical method for a 1-d inverse medium problem with experimental data. Inverse Problems and Imaging, 2016, 10 (4) : 1057-1085. doi: 10.3934/ipi.2016032 |
[15] |
Michael V. Klibanov, Thuy T. Le, Loc H. Nguyen, Anders Sullivan, Lam Nguyen. Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2021068 |
[16] |
El Mustapha Ait Ben Hassi, Salah-Eddine Chorfi, Lahcen Maniar, Omar Oukdach. Lipschitz stability for an inverse source problem in anisotropic parabolic equations with dynamic boundary conditions. Evolution Equations and Control Theory, 2021, 10 (4) : 837-859. doi: 10.3934/eect.2020094 |
[17] |
Sigve Hovda. Closed-form expression for the inverse of a class of tridiagonal matrices. Numerical Algebra, Control and Optimization, 2016, 6 (4) : 437-445. doi: 10.3934/naco.2016019 |
[18] |
Daniel Bouche, Youngjoon Hong, Chang-Yeol Jung. Asymptotic analysis of the scattering problem for the Helmholtz equations with high wave numbers. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1159-1181. doi: 10.3934/dcds.2017048 |
[19] |
Sergey V. Bolotin, Piero Negrini. Variational approach to second species periodic solutions of Poincaré of the 3 body problem. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 1009-1032. doi: 10.3934/dcds.2013.33.1009 |
[20] |
Victor Isakov, Joseph Myers. On the inverse doping profile problem. Inverse Problems and Imaging, 2012, 6 (3) : 465-486. doi: 10.3934/ipi.2012.6.465 |
2020 Impact Factor: 0.857
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