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Inverse Problems and Imaging (IPI)
 

A new Kohn-Vogelius type formulation for inverse source problems
Pages: 1051 - 1067, Issue 4, November 2015

doi:10.3934/ipi.2015.9.1051      Abstract        References        Full text (527.8K)           Related Articles

Xiaoliang Cheng - Department of Mathematics, Zhejiang University, Hangzhou 310027, China (email)
Rongfang Gong - Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China (email)
Weimin Han - Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States (email)

1 L. Afraites, M. Dambrine and D. Kateb, Conformal mappings and shape derivatives for the transmission problem with a single measurement, Numer. Func. Anal. Opt., 28 (2007), 519-551.       
2 K. Atkinson and W. Han, Theoretical Numerical Analysis: A Functional Analysis Framework, $3^{rd}$ edition, Springer-Verlag, New York, 2009.       
3 D. P. Bertsekas and E. M. Gafni, Projection method for variational inequalities with applications to the traffic assignment problem, Math. Prog. Study, 17 (1982), 139-159.       
4 R. W. Cottle, F. Giannessi and J. L. Lions, Variational Inequalities and Complementarity Problems: Theory and Applications, John Wiley and Sons, New York, 1980.       
5 L. C. Evans, Partial Differential Equations, American Mathematical Society, 1998.       
6 P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, 1985.       
7 W. Han, W. X. Cong and G. Wang, Mathematical theory and numerical analysis of bioluminescence tomography, Inverse Probl., 22 (2006), 1659-1675.       
8 W. Han, K. Kazmi, W. X. Cong and G. Wang, Bioluminescence tomography with optimized optical parameters, Inverse Probl., 23 (2007), 1215-1228.       
9 V. Isakov, Inverse Problems for Partial Differential Equations, Springer, New York, 1998.       
10 J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, 1971.       
11 C. Qin, J. Feng, S. Zhu, X. Ma, J. Zhong, P. Wu, Z. Jin and J. Tian, Recent advances in bioluminescence tomography: Methodology and system as well as application, Laser Photon. Rev., 8 (2014), 94-114.
12 S. J. Song and J. G. Huang, Solving an inverse problem from bioluminescence tomography by minimizing an energy-like functional, J. Comput. Anal. Appl., 14 (2012), 544-558.       
13 A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems, Wiley, New York, 1977.       

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