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Journal of Inverse and Ill-posed Problems, ISSN 0928-0219, 10/2017, Volume 25, Issue 5, pp. 669 - 685
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 2019, Volume 109, Issue 7, pp. 1611 - 1623
It has been recently shown that the nodal deficiency of an eigenfunction is encoded in the spectrum of the Dirichlet-to-Neumann operators for the... 
Nodal sets | Spectral indices | Nodal domains | Dirichlet-to-Neumann map | PHYSICS, MATHEMATICAL
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 09/2017, Volume 273, Issue 6, pp. 1970 - 2025
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2018, Volume 458, Issue 1, pp. 219 - 241
In the paper, we establish commutator estimates for the Dirichlet-to-Neumann map of Stokes systems in Lipschitz domains. The approach is based on Dahlberg's... 
Commutator estimate | Lipschitz domain | Dirichlet-to-Neumann map | Stokes system | MATHEMATICS | MATHEMATICS, APPLIED | ELLIPTIC-EQUATIONS | HOMOGENIZATION
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2019, Volume 475, Issue 2, pp. 1658 - 1684
In the present paper, we consider a non self adjoint hyperbolic operator with a vector field and an electric potential that depend not only on the space... 
Hyperbolic inverse problem | Time-dependent coefficient | Dirichlet-to-Neumann map | Stability estimate | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | WAVE-EQUATION
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 05/2019, Volume 44, Issue 5, pp. 367 - 396
We study the semiclassical microlocal structure of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a nonempty smooth boundary.... 
parametrix | transmission eigenvalues | Dirichlet-to-Neumann map | glancing region | MATHEMATICS | MATHEMATICS, APPLIED | TRANSMISSION | RESONANCES | Eigenvalues | Dirichlet problem | Riemann manifold | Asymptotic properties | Refraction | Smooth boundaries | Analysis of PDEs | Mathematics
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2015, Volume 259, Issue 11, pp. 5903 - 5926
The Dirichlet-to-Neumann map associated to an elliptic partial differential equation becomes multivalued when the underlying Dirichlet problem is not uniquely... 
Lipschitz domain | Neumann-to-Dirichlet map | Linear relation | Dirichlet-to-Neumann map | Schrödinger operator | MATHEMATICS | GENERALIZED RESOLVENTS | INEQUALITIES | EXTENSIONS | THEOREM | GLOBAL UNIQUENESS | Schrodinger operator | DIFFERENTIAL-OPERATORS
Journal Article
Inverse Problems, ISSN 0266-5611, 09/2017, Volume 33, Issue 10, p. 105006
This paper is focused on the study of an inverse problem for a non-self-adjoint hyperbolic equation. More precisely, we attempt to stably recover a first order... 
inverse problem | Carleman estimate | stability estimate | Dirichlet-to-Neumann map | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Mathematics - Analysis of PDEs
Journal Article
Optical and Quantum Electronics, ISSN 0306-8919, 6/2019, Volume 51, Issue 6, pp. 1 - 14
As an analog to graphene, honeycomb photonic crystals (PhCs) have attracted a great deal of interest in recent years. The additional degrees of freedom in a... 
Dirichlet-to-Neumann map | Photonic crystal | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Numerical method | Eigenvalue problem | Computer Communication Networks | Physics | Edge mode | Electrical Engineering | Waveguides | Graphene | Analysis | Graphite
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2017, Volume 49, Issue 2, pp. 756 - 776
In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect... 
Polygonal inclusion | Conductivity equation | Shape derivative | Dirichlet to Neumann map | TOMOGRAPHY | MATHEMATICS, APPLIED | INTERFACE | INVERSE CONDUCTIVITY PROBLEM | shape derivative | STABILITY | COEFFICIENTS | conductivity equation | polygonal inclusion | EQUATION
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 01/2014, Volume 39, Issue 1, pp. 120 - 145
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2014, Volume 267, Issue 7, pp. 2478 - 2506
We establish optimal conditions under which the G-convergence of linear elliptic operators implies the convergence of the corresponding Dirichlet to Neumann... 
Invisibility | Inverse conductivity problem | G-convergence | Dirichlet to Neumann map | MATHEMATICS | STABILITY | PLANE | GLOBAL UNIQUENESS | BOUNDARY
Journal Article
IMA Journal of Numerical Analysis, ISSN 0272-4979, 2014, Volume 34, Issue 3, pp. 1136 - 1155
In this work we consider the wave equation in homogeneous, unbounded domains and its numerical solution. In particular, we are interested in the effect that... 
time-domain Dirichlet-to-Neumann operator | linear multistep and Runge-Kutta methods | convolution quadrature | MULTISTEP | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | BOUNDARY INTEGRAL-OPERATORS | CONDITION NUMBER | BEM
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 06/2018, Volume 114, pp. 235 - 261
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 09/2017, Volume 273, Issue 6, pp. 2144 - 2166
We show that the fractional wave operator, which is usually studied in the context of hypersingular integrals but had not yet appeared in mathematical physics,... 
Nonlocal equations | Fractional wave operators | Anti-de Sitter spaces | Dirichlet-to-Neumann maps | LAPLACIAN | MATHEMATICS | CONSTANT | CONFORMAL GEOMETRY | EQUATION | EXTENSION PROBLEM
Journal Article
Advances in Mathematics, ISSN 0001-8708, 11/2015, Volume 285, pp. 1301 - 1338
The spectrum of a selfadjoint second order elliptic differential operator in L2(Rn) is described in terms of the limiting behavior of Dirichlet-to-Neumann... 
Boundary triple | Weyl function | Elliptic differential operator | Dirichlet-to-Neumann map | Spectral analysis | MATHEMATICS | GENERALIZED RESOLVENTS | EXTENSIONS | HAMILTONIAN-SYSTEMS | UNITARY EQUIVALENCE | BOUNDARY-VALUE-PROBLEMS
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2010, Volume 258, Issue 1, pp. 161 - 195
We consider the problem of stability estimate of the inverse problem of determining the magnetic field entering the magnetic Schrödinger equation in a bounded... 
Dirichlet-to-Neumann map | Schrödinger inverse problem | Magnetic field | Stability estimate | MATHEMATICS | SCATTERING PROBLEM | OPERATOR | GLOBAL UNIQUENESS | COEFFICIENTS | WAVE-EQUATION | Schrodinger inverse problem | HYPERBOLIC DIRICHLET | Magnetic fields | Universities and colleges
Journal Article
Journal of Geometric Analysis, ISSN 1050-6926, 7/2011, Volume 21, Issue 3, pp. 588 - 598
For maps from a domain Ω⊂ℝ m into a Riemannian manifold N, a functional coming from the norm of a fractional Sobolev space has recently been studied by Da Lio... 
35J50 | 58E20 | Mathematics | Abstract Harmonic Analysis | Fourier Analysis | Dirichlet-to-Neumann map | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | 35S99 | Differential Geometry | Dynamical Systems and Ergodic Theory | Harmonic map | Regularity | MATHEMATICS | FIELDS | SPHERE | SURFACE | WEAKLY HARMONIC MAPS | RIEMANNIAN-MANIFOLDS | UNIQUENESS
Journal Article
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