Journal of Inverse and Ill-posed Problems, ISSN 0928-0219, 10/2017, Volume 25, Issue 5, pp. 669 - 685

By our definition, “restricted Dirichlet-to-Neumann (DN) map” means that the Dirichlet and Neumann boundary data for a coefficient inverse problem (CIP) are...

global strict convexity, Carleman weight functions | convexification | 35R30 | Restricted Dirichlet-to-Neumann data | global strict convexity | Carleman weight functions | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | INVERSE PROBLEM | UNIQUENESS | Numerical analysis | Medical imaging | Land mines | Inverse problems | Mathematical analysis | Numerical methods | Uniqueness | Dirichlet problem | Fourier series | Electrical impedance | Mathematics - Numerical Analysis

global strict convexity, Carleman weight functions | convexification | 35R30 | Restricted Dirichlet-to-Neumann data | global strict convexity | Carleman weight functions | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | INVERSE PROBLEM | UNIQUENESS | Numerical analysis | Medical imaging | Land mines | Inverse problems | Mathematical analysis | Numerical methods | Uniqueness | Dirichlet problem | Fourier series | Electrical impedance | Mathematics - Numerical Analysis

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 09/2016, Volume 261, Issue 6, pp. 3551 - 3587

We introduce a generalized index for certain meromorphic, unbounded, operator-valued functions. The class of functions is chosen such that energy parameter...

Donoghue-type M-functions | Boundary triples | Index computations for meromorphic operator-valued functions | Weyl functions | Dirichlet-to-Neumann maps | Non-self-adjoint Schrödinger operators | ELLIPTIC DIFFERENTIAL-OPERATORS | UNITARY EQUIVALENCE | BOUNDARY-VALUE-PROBLEMS | LIPSCHITZ-DOMAINS | SELF-ADJOINT EXTENSIONS | SPACE | MATHEMATICS | Non-self-adjoint Schrodinger operators | RESOLVENTS | SYMMETRIC-OPERATORS | HERGLOTZ FUNCTIONS | SPECTRA

Donoghue-type M-functions | Boundary triples | Index computations for meromorphic operator-valued functions | Weyl functions | Dirichlet-to-Neumann maps | Non-self-adjoint Schrödinger operators | ELLIPTIC DIFFERENTIAL-OPERATORS | UNITARY EQUIVALENCE | BOUNDARY-VALUE-PROBLEMS | LIPSCHITZ-DOMAINS | SELF-ADJOINT EXTENSIONS | SPACE | MATHEMATICS | Non-self-adjoint Schrodinger operators | RESOLVENTS | SYMMETRIC-OPERATORS | HERGLOTZ FUNCTIONS | SPECTRA

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

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

A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator...

Dirichlet-to-Neumann map | Titchmarsh–Weyl m-function | Scattering matrix | Schrödinger operator | STRONG DELTA-INTERACTION | WEYL FUNCTIONS | ELLIPTIC DIFFERENTIAL-OPERATORS | Titchmarsh-Weyl m-function | PERTURBATION | BOUNDARY-VALUE-PROBLEMS | SELF-ADJOINT EXTENSIONS | SPECTRAL ASYMPTOTICS | MATHEMATICS | Schrodinger operator | RESOLVENT FORMULAS | DOMAINS | SCHRODINGER-OPERATORS

Dirichlet-to-Neumann map | Titchmarsh–Weyl m-function | Scattering matrix | Schrödinger operator | STRONG DELTA-INTERACTION | WEYL FUNCTIONS | ELLIPTIC DIFFERENTIAL-OPERATORS | Titchmarsh-Weyl m-function | PERTURBATION | BOUNDARY-VALUE-PROBLEMS | SELF-ADJOINT EXTENSIONS | SPECTRAL ASYMPTOTICS | MATHEMATICS | Schrodinger operator | RESOLVENT FORMULAS | DOMAINS | SCHRODINGER-OPERATORS

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

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

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

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 Computational and Applied Mathematics, ISSN 0377-0427, 03/2018, Volume 330, pp. 177 - 192

We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a...

Helmholtz problem | Dirichlet-to-Neumann map | Nonlinear eigenvalue problems | Scattering resonances | Matrix functions | Arnoldi’s method | Arnoldi's method | MATHEMATICS, APPLIED | MODES | P-VERSION | EIGENVALUE PROBLEMS | APPROXIMATION | FINITE-ELEMENT-METHOD | Poles | Scattering resonance | Switching systems | Matrix algebra | Numerical methods | Refractive index | Mathematics | Nonlinear eigenvalue problem | Finite element method | Helmholtz problems | Naturvetenskap | Arnoldi's methods | Resonance | Eigenvalues and eigenfunctions | Natural Sciences | Matematik

Helmholtz problem | Dirichlet-to-Neumann map | Nonlinear eigenvalue problems | Scattering resonances | Matrix functions | Arnoldi’s method | Arnoldi's method | MATHEMATICS, APPLIED | MODES | P-VERSION | EIGENVALUE PROBLEMS | APPROXIMATION | FINITE-ELEMENT-METHOD | Poles | Scattering resonance | Switching systems | Matrix algebra | Numerical methods | Refractive index | Mathematics | Nonlinear eigenvalue problem | Finite element method | Helmholtz problems | Naturvetenskap | Arnoldi's methods | Resonance | Eigenvalues and eigenfunctions | Natural Sciences | Matematik

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

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

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

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

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

Let (ℳ, g) be a compact Riemmanian manifold with non-empty boundary. Consider the second order hyperbolic initial-boundary value problem where is a first-order...

Hyperbolic inverse boundary value problem | Hyperbolic Dirichlet to Neumann map | Stability estimates | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | 35R30 | THEOREM | STABILITY | RECONSTRUCTION | BC-METHOD | 35L20 | MATHEMATICS | ANISOTROPIC MEDIA | RIGIDITY | GENERIC SIMPLE METRICS | INVERSE PROBLEMS | WAVE-EQUATION | Boundary value problems | Algorithms | Partial differential equations | Optimization | Boundaries

Hyperbolic inverse boundary value problem | Hyperbolic Dirichlet to Neumann map | Stability estimates | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | 35R30 | THEOREM | STABILITY | RECONSTRUCTION | BC-METHOD | 35L20 | MATHEMATICS | ANISOTROPIC MEDIA | RIGIDITY | GENERIC SIMPLE METRICS | INVERSE PROBLEMS | WAVE-EQUATION | Boundary value problems | Algorithms | Partial differential equations | Optimization | Boundaries

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

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

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

We give a new stability estimate for the problem of determining the time-dependent zero order coefficient in a parabolic equation from a partial parabolic...

Carleman inequality | Partial Dirichlet-to-Neumann map | Parabolic equation | Logarithmic stability | Semilinear parabolic equation | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | INVERSE PROBLEM | THEOREM | GLOBAL UNIQUENESS | DIFFERENTIAL-EQUATIONS | CALDERON PROBLEM | MATHEMATICS | STABLE DETERMINATION | HEAT-EQUATION | PARTIAL CAUCHY DATA | PARAMETER | Analysis of PDEs | Mathematics

Carleman inequality | Partial Dirichlet-to-Neumann map | Parabolic equation | Logarithmic stability | Semilinear parabolic equation | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | INVERSE PROBLEM | THEOREM | GLOBAL UNIQUENESS | DIFFERENTIAL-EQUATIONS | CALDERON PROBLEM | MATHEMATICS | STABLE DETERMINATION | HEAT-EQUATION | PARTIAL CAUCHY DATA | PARAMETER | Analysis of PDEs | Mathematics

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

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

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

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

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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