References
- Blum J. Numerical simulation and optimal control in plasma physics with application to Tokamaks. Modern applied mathematics. Chichester: Wiley; 1989.
- Lavrent’ev MM, Romanov VG, Shishat·skii SP. Ill-posed problems of mathematical physics and analysis. Vol. 64, Translations of mathematical monographs. Providence (RI): AMS; 1986.
- Alessandrini G. Stable determination of a crack from boundary measurements. Proc. Roy. Soc., Edinburgh Sect A. 1993;123:497–516.
- Bukhgeim AL, Cheng J, Yamamoto M. Stability for an inverse boundary problem of determining a part of a boundary. Inverse Prob. 1999;15:1021–1032.
- Cheng J, Prossdorf S, Yamamoto M. Local estimation for an integral equation of first kind with analytic kernel. Inverse Ill-Posed Prob. 1998;6:115–126.
- Inglese G. An inverse problem in corrosion detection. Inverse Prob. 1997;13:977–994.
- Colli-Franzone P, Magenes E. On the inverse potential problem of electrocardiology. Calcolo. 1979;16:459–538.
- Alessandrini G, Rondi L, Rosset E, Vessella S. The stability for the Cauchy problem for elliptic equations. Inverse Prob. 2009;25:1C47.
- Isakov V. Inverse problems for partial differential equations. Vol. 127, Applied mathematical sciences. New York (NY): Springer; 2006.
- Bourgeois L, Dardé J. About stability and regularization of ill-posed elliptic Cauchy problems: the case of Lipschitz domains. Appl. Anal. 2010;89:1745–1768.
- Bourgeois L, Dardé J. A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data. Inverse Prob. 2010;26:095016, 21pp.
- Cao H, Klibanov MV, Pereverzev SV. A Carleman estimate and the balancing principle in the quasi-reversibility method for solving the Cauchy problem for the Laplace equation. Inverse Prob. 2009;25:035005, 21pp.
- Klibanov MV, Timonov A. Carleman estimates for coefficient inverse problems and numerical applications. Utrecht: VSP; 2004.
- Klibanov MV. Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems. J. Inverse Ill-Posed Prob. 2013;21:477–560.
- Klibanov MV, Santosa F. A computational quasi-reversibility method for Cauchy problems for Laplace’s equation. SIAM J. Appl. Math. 1991;51:1653–1675.
- Lattes R, Lions JL. The method of quasi-reversibility: applications to partial differential equations. New York (NY): Elsevier; 1969.
- Hao DN, Lesnic D. The Cauchy for Laplace’s equation via the conjugate gradient method. IMA J. Appl. Math. 2000;65:199–217.
- Cheng J, Hon YC, Wei T, Yamamoto M. Numerical computation of a Cauchy problem for Laplace’s equation. ZAMM Z. Angew. Math. Mech. 2001;81:665–674.
- Hon YC, Wei T. Backus–Gilbert algorithm for the Cauchy problem of Laplace equation. Inverse Prob. 2001;17:261–271.
- Wei T, Qin HH, Shi R. Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation. Inverse Prob. 2008;24:035003, 18pp.
- Berntsson F, Elden L. Numerical solution of a Cauchy problem of Laplace equation. Inverse Prob. 2001;17:839–853.
- Xiong XT, Fu CL. Central difference regularization method for the Cauchy problem of the Laplace’s equation. Appl. Math. Comput. 2006;181:675–684.
- Wei T, Hon YC, Ling L. Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators. Eng. Anal. Bound. Elem. 2007;31:373–385.
- Sun Y, Zhang DY, Ma FM. A potential function method for the Cauchy problem of elliptic operators. J. Math. Anal. Appl. 2012;395:164–174.
- Zhang DY, Zhang GM, Zheng EX. The harmonic polynomial method for solving the Cauchy problem connected with the Laplace equation. Inverse Prob. 2013;29:065008, 17pp.
- Evans LC. Partial differential equations. Providence (RI): AMS; 1998.
- Calderon AP. Uniqueness in the Cauchy problem for partial differential equations. Am. J. Math. 1958;80:16–36.
- Chen G, Zhou J. Boundary element methods. London: Academic Press Limited; 1992.
- Hsiao GC, Wendland WL. Boundary integral equations. Berlin: Springer-Verlag; 2008.
- Kress R. Linear integral equations. Berlin: Springer-Verlag; 1989.