Inverse Boundary Spectral Problems

By A. Katchalov, Yaroslav Kurylev, Matti Lassas. 2001

413 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e79f77a8ec12eb919759bedaca969c0a3b57c831

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Mikko Salo
2. Gunther Uhlmann
3. Matti Lassas
4. G. Eskin
5. Carlos E. Kenig
6. Lauri Oksanen
7. Masahiro Yamamoto
8. Yaroslav Kurylev

In Computational Theory and Mathematics

1. Gunther Uhlmann
2. Mikko Salo
3. Matti Lassas
4. Masahiro Yamamoto
5. Lauri Oksanen
6. Yaroslav Kurylev
7. Carlos E. Kenig
8. David dos Santos Ferreira

In Mathematical Physics

1. Gunther Uhlmann
2. Mikko Salo
3. Matti Lassas
4. David dos Santos Ferreira
5. Masahiro Yamamoto
6. Yaroslav Kurylev
7. Carlos E. Kenig
8. Lauri Oksanen

Citations in the corpus

• Boundary regularity for the Ricci equation, geometric convergence, and Gel’fand’s inverse boundary problem (2002, methodology): “In [KKL] we use as coordinates some distance functions on M .”
• Inverse Hyperbolic Problems with Time-Dependent Coefficients (2005, methodology): “The most general results were obtained by the BC-methods in the case of self-adjoint hyperbolic operators with time-independent coefficients (see Belishev, 1997a, 2002; Katchalov and Kurylev, 1998; Katchalov et al., 2001; Kurylev, 1993).”
• The Calderón problem with partial data on manifolds and applications (2012, background): “(7-4) Choosing H(t0)= H0, where H0 is a complex symmetric matrix with Im(H0) positive definite, it follows that the Riccati equation has a unique smooth complex symmetric solution H(t) with Im(H(t)) positive definite; see [Katchalov et al. 2001].”
• Rigidity of broken geodesic flow and inverse problems (2007, background): “[5], [26], [29] that the setR(M) possesses a natural structure of a Riemannian manifold with the map”
• Stability estimate for the hyperbolic inverse boundary value problem by local Dirichlet-to-Neumann map (2008, background): “, Belishev [1], Katchalov, Kurylev and Lassas [15], Kurylev and Lassas [18]).”
• Stable determination of generic simple metrics from the hyperbolic Dirichlet-to-Neumann map (2004, result): “We also refer to [KKL1], [B2], [KKLM] and the references therein for more uniqueness results in this direction.”
• Carleman estimates for parabolic equations and applications (2009, neutral): “However, the inverse problems by the Dirichlet-to-Neumann map are outside the scope of this review and see e.g., a monograph by Isakov [90], Katchlov et al [95] as reference books.”
• The Calderón problem in transversally anisotropic geometries (2013, methodology): “This follows from the boundary control method introduced by Belishev [3] and later developed by several authors; we refer to the book [18] for further details.”
• Global uniqueness in an inverse problem for time fractional diffusion equations (2016, methodology): “Following [13, 14, 31], we define the boundary spectral data associated with (ρ, a, V ), as”