Faouzi Triki1, Tao Yin2
[1] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, volume 224, springer, 2015. [2] H. Ammari, J. Garnier, H. Kang, L.H. Nguyen and L. Seppecher, Multi-Wave Medical Imaging:Mathematical Modelling & Imaging Reconstruction, World Scientific, London, 2017. [3] M. Choulli and F. Triki, New stability estimates for the inverse medium problem with internal data, SIAM J. Math. Anal, 47:3(2015), 1778-1799. [4] G. Bal and G. Uhlmann, Reconstruction of coefficients in scalar second-order elliptic equations from knowledge of their solutions, Comm. Pure Appl. Math., 66:10(2013), 1629-1652. [5] E. Bonnetier, M. Choulli and F. Triki, Stability for quantitative photoacoustic tomography revisited. Res. Math. Sci., 9:24(2022). [6] G. Bal and K. Ren, Multi-source quantitative photoacoustic tomography in a diffusive regime, Inverse Problems, 27:7(2011), 075003. [7] W. Naetar and O. Scherzer, Quantitative photoacoustic tomography with piecewise constant material parameters, SIAM Journal on Imaging Sciences, 7:3(2014), 1755-1774. [8] M. Briane, Reconstruction of isotropic conductivities from non smooth electric fields, ESAIM:Math. Model. Numer. Anal., 52:3(2018), 1173-1193. [9] M. Briane, G.W. Milton and A. Treibergs, Which electric fields are realizable in conducting materials, ESAIM:Math. Model. Numer. Anal., 48:2(2014), 307-323. [10] M. Choulli and E. Zuazua, Lipschitz dependence of the coefficients on the resolvent and greedy approximation for scalar elliptic problems, C. R. Math. Acad. Sci. Paris, Ser I, 354(2016), 1174-1187. [11] P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods, SIAM J. Math. Anal., 43:3(2011), 1457-1472. [12] P. Pavel and J. Sokolowski, Compressible Navier-Stokes equations:theory and shape optimization, Birkhäuser Basel, 2012. [13] G. Fichera, Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Nat. Sez. I, 5:8(1956), 1-30. [14] J.J. Kohn and L. Nirenberg, Degenerate elliptic-parabolic equations of second order, Comm. Pure Appl. Math., 20(1967), 797-872. [15] O.A. Oleinik and E.V. Radkevic, Second Order Equations with Nonnegative Characteristic Form, Plenum Press, New York, 1973. [16] G.R. Richter, An inverse problem for the steady state diffusion equation, SIAM Journal on Applied Mathematics, 41:2(1981), 210-221. [17] K.O. Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math., 11(1958), 333-418. [18] A. Ern, J.L. Guermond and G. Caplain, An intrinsic criterion for the bijectivity of hilbert operators related to friedrichs' systems, Communications in Partial Differential Equations, 32(2007), 317- 341. [19] N. Antonić and K. Burazin, Intrinsic boundary conditions for friedrichs systems, Communications in Partial Differential Equations, 35:9(2010), 1690-1715. [20] D.A.D. Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, Mathématiques & Applications, Springer-Verlag, 2012. [21] G. Alessandrini, An identification problem for an elliptic equation in two variables, Annalidi Matematica Pura ed Applicata, 145(1986), 265-295. [22] R.A. Adams and J.F. Fournier, Sobolev Spaces (Second ed.), Academic Press, 2003. [23] B. Rivière, Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations:Theory and Implementation, SIAM, 2008. [24] N. Garofalo and F.H. Lin, Monotonicity properties of variational integrals, ap weights and unique continuation, Indiana Univ. Math. J., 35:2(1986), 245-268. |
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