References
- Balanis CA. Antenna theory – analysis and design. Hoboken (NJ): Wiley; 2005.
- Ammari H, Bao G, Fleming J. Inverse source problem for Maxwell's equation in magnetoencephalography. SIAM J Appl Math. 2002;62:1369–1382. doi: https://doi.org/10.1137/S0036139900373927
- Isakov V. Inverse problems for partial differential equations. New York (NY): Springer-Verlag; 2017.
- Eller M, Valdivia NP. Acoustic source identification using multiple frequency information. Inverse Probl. 2009;25:115005 (20pp). doi: https://doi.org/10.1088/0266-5611/25/11/115005
- Bao G, Lin J, Triki F. A multi-frequency inverse source problem. J Differ Equ. 2010;249:3443–3465. doi: https://doi.org/10.1016/j.jde.2010.08.013
- Cheng J, Isakov V, Lu S. Increasing stability in the inverse source problem with many frequencies. J Differ Equ. 2016;260:4786–4804. doi: https://doi.org/10.1016/j.jde.2015.11.030
- Isakov V, Lu S. On the inverse source problem with boundary data at many wave numbers. In: Inverse problems and related topics (Chapter 4). 2020. (Springer proceedings in mathematics and statistics; 310), 59–80.
- Isakov V, Lu S. Increasing stability in the inverse source problem with attenuation and many frequencies. SIAM J Appl Math. 2018;78:1–18. doi: https://doi.org/10.1137/17M1112704
- Entekhabi M, Isakov V. Increasing stability in acoustic and elastic inverse source problems, arXiv 1808.10528 (submitted for publication).
- Isakov V, Lu S. Inverse source problems without (pseudo)convexity assumptions. Inverse Probl Imaging. 2018;12:955–970. doi: https://doi.org/10.3934/ipi.2018040
- John F. Continuous dependence on data for solutions of partial differential equations with a prescribed bound. Comm Pure Appl Math. 1960;13:551–587. doi: https://doi.org/10.1002/cpa.3160130402
- Isakov V. On increasing stability in the continuation for elliptic equations of second order without (pseudo) convexity assumptions. Inverse Probl Imaging. 2019;13:983–1006. doi: https://doi.org/10.3934/ipi.2019044
- Isakov V. Increasing stability for the Schrödinger potential from the Dirichlet-to-Neumann map. Discrete Contin Dyn Syst. 2011;4:631–641. doi: https://doi.org/10.3934/dcdss.2011.4.631
- Isakov V, Wang J-N. Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to-Neumann map. Inverse Probl Imaging. 2014;8:1139–1150. doi: https://doi.org/10.3934/ipi.2014.8.1139
- Isakov V, Lu S, Xu B. Linearized inverse Schrödinger potential problem at a large wave number. SIAM J Appl Math. 2020;80:338–358. doi: https://doi.org/10.1137/18M1226932
- Isakov V, Lai R-Y, Wang J-N. Increasing stability for conductivity and attenuation coefficients. SIAM J Math Anal. 2016;48:569–594. doi: https://doi.org/10.1137/15M1019052
- Entekhabi M, Isakov V. On increasing stability in the two dimensional inverse source scattering problem with many frequencies. Inverse Probl. 2018;34:05505.
- Isakov V. General hyperbolic diffraction problems. AMS; 1977. (Trudy Sobolev Seminar).
- Lions JL, Magenes E. Non-homogeneous boundary value problems and applications. Vol. I. New York (NY): Springer-Verlag; 1972.
- Lasiecka I, Triggiani R, Yao P-F. Inverse/observability estimates for second-order hyperbolic equations with variable coefficients. J Math Anal Appl. 1999;235:13–57. doi: https://doi.org/10.1006/jmaa.1999.6348
- Tataru D. Carleman estimates and unique continuation for solutions to boundary value problems. J Math Pures Appl. 1996;75:367–408.
- Eller M, Isakov V, Nakamura G, et al. Uniqueness and stability in the Cauchy problem for Maxwell' and elasticity systems. In: Cioranescu D and Lions J-L, editors. Nonlinear partial differential equations and their applications. North-Holland: Elsevier Science; 2002. p. 329–351.