References
- Carleman T. Sur un problème d’unicité pour les systèmes d’équations aux dérivées partielles à deux variables indépendentes [On a problem of the uniqueness for systems of partial differential equations with two independent variables]. Ark. Mat. Astr. Fys. 1939;26B:1–9.
- Hörmander L. Linear partial differential operators. Berlin: Springer-Verlag; 1963.
- Imanuvilov OY. On Carleman estimates for hyperbolic equations. Asymptot. Anal. 2002;32:185–220.
- Imanuvilov OY, Yamamoto M. Carleman estimate for a stationary isotropic Lamé system and the applications. Applicable Anal. 2004;83:243–270.
- Isakov V. Carleman type estimates in an anisotropic case and applications. J. Differ. Equ. 1993;105:217–239.
- Isakov V. Inverse problems for partial differential equations. Berlin: Springer-Verlag; 2006.
- Khaĭdarov A. Carleman estimates and inverse problems for second order hyperbolic equations. Math. USSR Sbornik. 1987;58:267–277.
- Klibanov MV. Inverse problems and Carleman estimates. Inverse Probl. 1992;8:575–596.
- Klibanov MV, Timonov A. Carleman estimates for coefficient inverse problems and numerical applications. Utrect: VSP; 2004.
- Lavrent’ev MM, Romanov VG, Shishatskii SP. Ill-posed problems of mathematical physics and analysis. Providence (RI): American Mathematical Society; 1986.
- Nirenberg L. Lectures on linear partial diffirential equations. In: Conference Board in the Mathematical Sciences Regional Conference. Vol. 17; Providence, RI: AMS; 1973.
- Romanov VG. Carleman estimates for second-order hyperbolic equations. Sib. Math. J. 2006;47:135–151.
- Tataru D. Carleman estimates and unique continuation for solutions to boundary value problems. J. Math. Pures Appl. 1996;75:367–408.
- Kazemi A, Klibanov MV. Stability estimates for ill-posed Cauchy problems involving hyperbolic equations and inequalities. Appl. Anal. 1993;50:93–102.
- Klibanov MV. Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems. J. Inverse Ill-Posed Probl. 2013;21:477–560.
- Beilina L, Klibanov MV. Approximate global convergence and adaptivity for coefficient Inverse problems. New York (NY): Springer; 2012.
- Bellassoued M, Imanuvilov O, Yamamoto M. Inverse problem of determining the density and two Lamé coefficients by boundary data. SIAM J. Math. Anal. 2008;40:238–265.
- Bukhgeim AL. Introduction to the theory of inverse problems. Utrecht: VSP; 2000.
- Bukhgeim AL, Klibanov MV. Global uniqueness of a class of multidimensional inverse problems. Soviet Math. Dokl. 1981;24:244–247.
- Imanuvilov OY, Isakov V, Yamamoto M. An inverse problem for the dynamical Lamé system with two sets of boundary data. Commun. Pure Appl. Math. 2003;56:1366–1382.
- Imanuvilov OY, Yamamoto M. Global Lipschitz stability in an inverse hyperbolic problem by interior observations. Inverse Probl. 2001;17:717–728.
- Imanuvilov OY, Yamamoto M. Determination of a coefficient in an acoustic equation with a single measurement. Inverse Probl. 2003;19:157–171.
- Klibanov MV. Uniqueness of solutions of two inverse problems for the Maxwellian system, USSR. J. Comput. Math, Math. Phys. 1986;26:1063–1071.
- Yamamoto M. On an inverse problem of determining source terms in Maxwell’s equations with a single measurement. Inverse problems, tomography, and image processing. Vol. 15. New York (NY): Plenum Press 1998. p. 241–256.
- Yamamoto M. Uniqueness and stability in multidimensional hyperbolic inverse problems. J. Math. Pures Appl. 1999;78:65–98.
- Isakov V, Nakamura G, Wang J-N. Uniqueness and stability in the Cauchy problem for the elasticity system with residual stress. In: Giovanni A, Gunther U, editors. Inverse problem: theory and applications. Vol. 333, Contemporary mathematics. Providence (RI): AMS; 2003. p. 99–113.
- Egorov YUV. Linear differential equations of principal type. New York (NY): Consultants to Bureau; 1986.
- Isakov V, Wang J-N, Yamamoto M. An inverse problem for dynamical Lamé system with residual stress. SIAM J. Math. Anal. 2007;39:1328–1343.
- Eller M, Yamamoto M. A Carleman inequality for the stationary anisotropic Maxwell system. J. Math. Pures Appl. 2006;86:449–462.
- Kong JA. Electromagnetic wave theory. New York (NY): John-Wiley; 1990.
- Bellassoued M, Cristofol M, Soccorsi E. Inverse boundary value problem for the dynamical heterogeneous Maxwell’s system. Inverse Probl. 2012;28:095009.
- Li S. An inverse problem for Maxwell’s equations in bi-isotropic media. SIAM J. Math. Anal. 2005;37:1027–1043.
- Li S, Yamamoto M. An inverse problem for Maxwell’s equations in anisotropic media. Chin. Ann. Math. Ser. B. 2007;28B:35–54.
- Li S, Yamamoto M. An inverse problem for Maxwell’s equations in isotropic and non-stationary media. Appl. Anal. 2013;92:2335–2356.
- Li S. Carleman estimates for second order hyperbolic systems in anisotropic cases and an inverse source problem. Part II: an inverse source problem. Appl. Anal. Available from: http://dx.doi.org/10.1080/00036811.2014.986847
- Adams RA, Fournier JJF. Sobolev spaces. New York (NY): Academic Press; 2003.
- Lions J-L, Magenes E. Non-homogeneous boundary value problems and applications. Berlin: Springer; 1972.