Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2016, Volume 368, Issue 9, pp. 6227 - 6252

We consider second order uniformly elliptic operators of divergence form in \mathbb{R}^{d+1} H^s(\mathbb{R}^d) . Moreover, we also show a factorization formula...

Dirichlet-Neumann maps | CALCULUS | EQUATIONS | PSEUDODIFFERENTIAL-OPERATORS | DIRAC OPERATORS | ABSOLUTE CONTINUITY | L-P | LAYER POTENTIALS | Divergence form elliptic operators | MATHEMATICS | BILINEAR ESTIMATE | NONSMOOTH COEFFICIENTS | Poisson operators | DOMAINS

Dirichlet-Neumann maps | CALCULUS | EQUATIONS | PSEUDODIFFERENTIAL-OPERATORS | DIRAC OPERATORS | ABSOLUTE CONTINUITY | L-P | LAYER POTENTIALS | Divergence form elliptic operators | MATHEMATICS | BILINEAR ESTIMATE | NONSMOOTH COEFFICIENTS | Poisson operators | DOMAINS

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 09/2014, Volume 272, pp. 266 - 278

The propagation of linear elastic waves arises in a wide array of applications, for instance, in mechanical engineering, materials science, and the...

Navier's equation | Linear elastodynamics | High-order spectral methods | Dirichlet–Neumann operators | Boundary perturbation methods | Dirichlet-Neumann operators | IMPROVED FORMALISM | SHAPE DEFORMATIONS | DIFFRACTION PROBLEMS | PHYSICS, MATHEMATICAL | SEISMIC-WAVE PROPAGATION | SPECTRAL-ELEMENT SIMULATIONS | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ROUGH-SURFACE SCATTERING | PERTURBATION THEORIES | ELECTROMAGNETIC-WAVES | ITERATIVE-SERIES | Operators | Wave propagation | Perturbation methods | Computation | Boundaries | Elastodynamics | Traction | Arrays

Navier's equation | Linear elastodynamics | High-order spectral methods | Dirichlet–Neumann operators | Boundary perturbation methods | Dirichlet-Neumann operators | IMPROVED FORMALISM | SHAPE DEFORMATIONS | DIFFRACTION PROBLEMS | PHYSICS, MATHEMATICAL | SEISMIC-WAVE PROPAGATION | SPECTRAL-ELEMENT SIMULATIONS | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ROUGH-SURFACE SCATTERING | PERTURBATION THEORIES | ELECTROMAGNETIC-WAVES | ITERATIVE-SERIES | Operators | Wave propagation | Perturbation methods | Computation | Boundaries | Elastodynamics | Traction | Arrays

Journal Article

SIAM JOURNAL ON NUMERICAL ANALYSIS, ISSN 0036-1429, 2019, Volume 57, Issue 3, pp. 1183 - 1204

The computation of the Dirichlet-Neumann operator for the Laplace equation is the primary challenge for the numerical simulation of the ideal fluid equations....

Zernike polynomials | WATER-WAVES | MATHEMATICS, APPLIED | POLAR | EQUATIONS | SURFACE | Euler equations | Dirichlet-Neumann operator

Zernike polynomials | WATER-WAVES | MATHEMATICS, APPLIED | POLAR | EQUATIONS | SURFACE | Euler equations | Dirichlet-Neumann operator

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 04/2018, Volume 474, Issue 2212, p. 20170704

The faithful modelling of the propagation of linear waves in a layered, periodic structure is of paramount importance in many branches of the applied sciences....

Impedance–impedance operators | Helmholtz equation | Diffraction gratings | Linear wave scattering | High-order perturbation of surfaces methods | Layered media | DIRICHLET-NEUMANN OPERATORS | ACOUSTIC SCATTERING | layered media | MULTIDISCIPLINARY SCIENCES | SHAPE DEFORMATIONS | linear wave scattering | diffraction gratings | DIFFRACTION PROBLEMS | NUMERICAL-SOLUTION | BOUNDARIES | impedance-impedance operators | high-order perturbation of surfaces methods | ROUGH-SURFACE SCATTERING | PERIODIC GRATINGS | GREEN-FUNCTION | METALLIC-FILMS | 1008 | impedance–impedance operators | 1009

Impedance–impedance operators | Helmholtz equation | Diffraction gratings | Linear wave scattering | High-order perturbation of surfaces methods | Layered media | DIRICHLET-NEUMANN OPERATORS | ACOUSTIC SCATTERING | layered media | MULTIDISCIPLINARY SCIENCES | SHAPE DEFORMATIONS | linear wave scattering | diffraction gratings | DIFFRACTION PROBLEMS | NUMERICAL-SOLUTION | BOUNDARIES | impedance-impedance operators | high-order perturbation of surfaces methods | ROUGH-SURFACE SCATTERING | PERIODIC GRATINGS | GREEN-FUNCTION | METALLIC-FILMS | 1008 | impedance–impedance operators | 1009

Journal Article

5.
Full Text
Maximal parabolic regularity for divergence operators including mixed boundary conditions

Journal of Differential Equations, ISSN 0022-0396, 2009, Volume 247, Issue 5, pp. 1354 - 1396

We show that elliptic second order operators of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is...

Quasilinear parabolic equations | Mixed Dirichlet–Neumann conditions | Maximal parabolic regularity | Mixed Dirichlet-Neumann conditions | ELLIPTIC DIFFERENTIAL-OPERATORS | SPACES | SIMPLE EXCLUSION PROCESS | EVOLUTION-EQUATIONS | LIPSCHITZ-DOMAINS | L-P | TRANSMISSION PROBLEMS | MATHEMATICS | PHASE SEGREGATION DYNAMICS | PARTICLE-SYSTEMS | LONG-RANGE INTERACTIONS

Quasilinear parabolic equations | Mixed Dirichlet–Neumann conditions | Maximal parabolic regularity | Mixed Dirichlet-Neumann conditions | ELLIPTIC DIFFERENTIAL-OPERATORS | SPACES | SIMPLE EXCLUSION PROCESS | EVOLUTION-EQUATIONS | LIPSCHITZ-DOMAINS | L-P | TRANSMISSION PROBLEMS | MATHEMATICS | PHASE SEGREGATION DYNAMICS | PARTICLE-SYSTEMS | LONG-RANGE INTERACTIONS

Journal Article

Inverse Problems, ISSN 0266-5611, 07/2017, Volume 33, Issue 9, p. 95001

In this paper we prove identifiability and stability estimates for a local-data inverse boundary value problem for a magnetic Schrodinger operator in dimension...

Carleman estimates | DirichletNeumann map | complex geometric optics solutions | RiemannLebesgue lemma | fourier transform | Magnetic Schrödinger operator | MATHEMATICS, APPLIED | Riemann-Lebesgue lemma | INVERSE PROBLEM | Dirichlet-Neumann map | Magnetic Schrodinger operator | PHYSICS, MATHEMATICAL | EQUATION | UNIQUENESS

Carleman estimates | DirichletNeumann map | complex geometric optics solutions | RiemannLebesgue lemma | fourier transform | Magnetic Schrödinger operator | MATHEMATICS, APPLIED | Riemann-Lebesgue lemma | INVERSE PROBLEM | Dirichlet-Neumann map | Magnetic Schrodinger operator | PHYSICS, MATHEMATICAL | EQUATION | UNIQUENESS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 8/2008, Volume 360, Issue 8, pp. 3945 - 3973

Operators of the form A = a(x,D) + K with a pseudodifferential symbol a(x,ξ) belonging to the Hörmander class $S_{1,\delta}^{m}$ , m > 0, 0 ≤ δ < 1, and...

Mathematical manifolds | Riemann manifold | Differential operators | Evolution equations | Fourier transformations | Coordinate systems | Calculus | Banach space | Sobolev spaces | Dirichlet-Neumann operator | Bounded H∞-calculus | Pseudodifferential operators

Mathematical manifolds | Riemann manifold | Differential operators | Evolution equations | Fourier transformations | Coordinate systems | Calculus | Banach space | Sobolev spaces | Dirichlet-Neumann operator | Bounded H∞-calculus | Pseudodifferential operators

Journal Article

INVERSE PROBLEMS AND IMAGING, ISSN 1930-8337, 12/2018, Volume 12, Issue 6, pp. 1309 - 1342

In this paper we study local stability estimates for a magnetic Schrodinger operator with partial data on an open bounded set in dimension n >= 3. This is the...

MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | INVERSE PROBLEM | magnetic Schrodinger operator | Dirichlet-Neumann map | Carleman estimates | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | complex geometric optic solutions | Inverse problems | Radon transform | PARTIAL CAUCHY DATA | EQUATION

MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | INVERSE PROBLEM | magnetic Schrodinger operator | Dirichlet-Neumann map | Carleman estimates | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | complex geometric optic solutions | Inverse problems | Radon transform | PARTIAL CAUCHY DATA | EQUATION

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 09/2016, Volume 321, pp. 414 - 434

We present a new numerical method to simulate the time evolution of axisymmetric nonlinear waves on the surface of a ferrofluid jet. It is based on the...

Series expansion | Pseudo-spectral method | Dirichlet–Neumann operator | Solitary waves | Ferrofluid jet | Dirichlet-Neumann operator | DIRICHLET-NEUMANN OPERATORS | GRAVITY-WAVES | PHYSICS, MATHEMATICAL | FLOW | ANALYTICITY | WATER-WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DEEP-WATER | DOMAINS | SCATTERING | Magnetic fields | Analysis | Methods

Series expansion | Pseudo-spectral method | Dirichlet–Neumann operator | Solitary waves | Ferrofluid jet | Dirichlet-Neumann operator | DIRICHLET-NEUMANN OPERATORS | GRAVITY-WAVES | PHYSICS, MATHEMATICAL | FLOW | ANALYTICITY | WATER-WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DEEP-WATER | DOMAINS | SCATTERING | Magnetic fields | Analysis | Methods

Journal Article

Asymptotic Analysis, ISSN 0921-7134, 2017, Volume 104, Issue 3-4, pp. 103 - 106

We consider the elliptic estimates for the Dirichlet-Neumann operator related to the water waves problem on a two-dimensional corner domain in this paper. Due...

corner domains | Elliptic estimate | water waves problem | Dirichlet-Neumann operator | PLANE DOMAINS | MATHEMATICS, APPLIED | 2ND-ORDER | GENERAL EDGE ASYMPTOTICS | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | WELL-POSEDNESS | WAVES | STABLE ASYMPTOTICS | COEFFICIENTS | POINTS | Water waves | Dirichlet problem | Estimates

corner domains | Elliptic estimate | water waves problem | Dirichlet-Neumann operator | PLANE DOMAINS | MATHEMATICS, APPLIED | 2ND-ORDER | GENERAL EDGE ASYMPTOTICS | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | WELL-POSEDNESS | WAVES | STABLE ASYMPTOTICS | COEFFICIENTS | POINTS | Water waves | Dirichlet problem | Estimates

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2010, Volume 47, Issue 6, pp. 4540 - 4568

In this paper, the tight relationship between Dirichlet—Neumann (D-N) operators and optimized Schwarz methods with Robin transmission conditions is disclosed....

Spectroscopy | Degrees of freedom | Triangulation | Mathematical theorems | Spectral theory | Decomposition methods | Linear transformations | Polyhedrons | Perceptron convergence procedure | Convergence rate | Finite elements | Optimized Schwarz methods with Robin transmission conditions | Dirichlet-Neumann operators | Nonoverlapping domain decomposition | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | DOMAIN DECOMPOSITION METHOD | EQUATIONS | COEFFICIENTS | convergence rate | optimized Schwarz methods with Robin transmission conditions | finite elements | nonoverlapping domain decomposition | Operators | Spectra | Numerical analysis | Asymptotic properties | Convergence

Spectroscopy | Degrees of freedom | Triangulation | Mathematical theorems | Spectral theory | Decomposition methods | Linear transformations | Polyhedrons | Perceptron convergence procedure | Convergence rate | Finite elements | Optimized Schwarz methods with Robin transmission conditions | Dirichlet-Neumann operators | Nonoverlapping domain decomposition | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | DOMAIN DECOMPOSITION METHOD | EQUATIONS | COEFFICIENTS | convergence rate | optimized Schwarz methods with Robin transmission conditions | finite elements | nonoverlapping domain decomposition | Operators | Spectra | Numerical analysis | Asymptotic properties | Convergence

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2005, Volume 37, Issue 1, pp. 302 - 320

In this paper we take up the question of analyticity properties of Dirichlet - Neumann operators with respect to boundary deformations. In two separate...

Sobolev regularity | Hölder regularity | Boundary value problems | Geometric perturbations | Dirichlet-Neumann operators | Free-boundary problems | MATHEMATICS, APPLIED | free-boundary problems | STABILITY | boundary value problems | SHAPE DEFORMATIONS | ROUGH-SURFACE SCATTERING | Holder regularity | GRAVITY WATER-WAVES | CONTINUATION | geometric perturbations

Sobolev regularity | Hölder regularity | Boundary value problems | Geometric perturbations | Dirichlet-Neumann operators | Free-boundary problems | MATHEMATICS, APPLIED | free-boundary problems | STABILITY | boundary value problems | SHAPE DEFORMATIONS | ROUGH-SURFACE SCATTERING | Holder regularity | GRAVITY WATER-WAVES | CONTINUATION | geometric perturbations

Journal Article

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, ISSN 1078-0947, 10/2019, Volume 39, Issue 10, pp. 6039 - 6067

Based on the H-2 existence of the solution, we investigate weighted estimates for a mixed boundary elliptic system in a two-dimensional corner domain, when the...

MATHEMATICS | MATHEMATICS, APPLIED | 2ND-ORDER | GENERAL EDGE ASYMPTOTICS | corner domain | mixed boundary problem | COEFFICIENTS | Weighted elliptic estimates | Dirichlet-Neumann operator

MATHEMATICS | MATHEMATICS, APPLIED | 2ND-ORDER | GENERAL EDGE ASYMPTOTICS | corner domain | mixed boundary problem | COEFFICIENTS | Weighted elliptic estimates | Dirichlet-Neumann operator

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2001, Volume 170, Issue 1, pp. 276 - 298

In this paper we present results on the stability of perturbation methods for the evaluation of Dirichlet-Neumann operators (DNO) defined on domains that are...

Dirichlet-Neumann operators | Numerical stability | Geometric perturbation methods | WATER-WAVES | IMPROVED FORMALISM | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | geometric perturbation methods | GRAVITY-WAVES | BOUNDARY | ROUGH-SURFACE SCATTERING | PHYSICS, MATHEMATICAL | numerical stability | EQUATION

Dirichlet-Neumann operators | Numerical stability | Geometric perturbation methods | WATER-WAVES | IMPROVED FORMALISM | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | geometric perturbation methods | GRAVITY-WAVES | BOUNDARY | ROUGH-SURFACE SCATTERING | PHYSICS, MATHEMATICAL | numerical stability | EQUATION

Journal Article

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9947, 2008, Volume 360, Issue 8, pp. 3945 - 3973

Operators of the form A = a( x, D) + K with a pseudodifferential symbol a( x, xi) belonging to the Hormander class S-1,delta(m), m > 0, 0 <= delta < 1, and...

MATHEMATICS | pseudodifferential operators | bounded H-infinity-calculus | Dirichlet-Neumann operator

MATHEMATICS | pseudodifferential operators | bounded H-infinity-calculus | Dirichlet-Neumann operator

Journal Article

ANALYSIS AND APPLICATIONS, ISSN 0219-5305, 04/2012, Volume 10, Issue 2

In this paper, we prove L-infinity-estimates for solutions of divergence operators in the case of mixed boundary conditions. In this very general setting, the...

MATHEMATICS | MATHEMATICS, APPLIED | CAMPANATO SPACES | Elliptic equations | BOUNDARY-VALUE-PROBLEMS | L-infinity-estimates | NONSMOOTH DATA | mixed Dirichlet-Neumann conditions

MATHEMATICS | MATHEMATICS, APPLIED | CAMPANATO SPACES | Elliptic equations | BOUNDARY-VALUE-PROBLEMS | L-infinity-estimates | NONSMOOTH DATA | mixed Dirichlet-Neumann conditions

Journal Article

Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, 6/2008, Volume 10, Issue 2, pp. 238 - 271

In this paper we take up the question of analyticity properties of Dirichlet–Neumann operators (DNO) which arise in boundary value and free boundary problems...

boundary perturbation methods | Dirichlet–Neumann operators | geometric perturbation | 76B15 | water waves | 76B07 | 35J05 | Physics | Mechanics, Fluids, Thermodynamics | Mathematical Methods in Physics | Fluids | free-boundary problems | 35Q35 | boundary value problems | Water waves | Boundary value problems | Dirichlet-Neumann operators | Free-boundary problems | Geometric perturbation | Boundary perturbation methods | PHYSICS, FLUIDS & PLASMAS | SHAPE DEFORMATIONS | WATER-WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ROUGH-SURFACE SCATTERING | NUMERICAL-SIMULATION

boundary perturbation methods | Dirichlet–Neumann operators | geometric perturbation | 76B15 | water waves | 76B07 | 35J05 | Physics | Mechanics, Fluids, Thermodynamics | Mathematical Methods in Physics | Fluids | free-boundary problems | 35Q35 | boundary value problems | Water waves | Boundary value problems | Dirichlet-Neumann operators | Free-boundary problems | Geometric perturbation | Boundary perturbation methods | PHYSICS, FLUIDS & PLASMAS | SHAPE DEFORMATIONS | WATER-WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ROUGH-SURFACE SCATTERING | NUMERICAL-SIMULATION

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 3, pp. 906 - 920

This paper presents an accurate and stable numerical scheme for computation of the first variation of the Dirichlet–Neumann operator in the context of Euler’s...

Water waves | Boundary Perturbation methods | Dirichlet–Neumann operators | Functional variations | High-order/spectral methods | Dirichlet-Neumann operators | IMPROVED FORMALISM | TRAVELING WATER-WAVES | SINGULARITIES | STABILITY | DIFFRACTION PROBLEMS | 3 DIMENSIONS | PHYSICS, MATHEMATICAL | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BOUNDARIES | SCATTERING | CONTINUATION | Analysis | Algorithms

Water waves | Boundary Perturbation methods | Dirichlet–Neumann operators | Functional variations | High-order/spectral methods | Dirichlet-Neumann operators | IMPROVED FORMALISM | TRAVELING WATER-WAVES | SINGULARITIES | STABILITY | DIFFRACTION PROBLEMS | 3 DIMENSIONS | PHYSICS, MATHEMATICAL | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BOUNDARIES | SCATTERING | CONTINUATION | Analysis | Algorithms

Journal Article

Siberian Mathematical Journal, ISSN 0037-4466, 3/2013, Volume 54, Issue 2, pp. 271 - 300

Under consideration is the Dirichlet-Neumann operator on the boundary of the distorted half-space bounded below by a surface which is close to a hyperplane. We...

Mathematics, general | Mathematics | Dirichlet-Neumann operator | differential | MATHEMATICS | EQUATIONS | WATER-WAVES | WELL-POSEDNESS

Mathematics, general | Mathematics | Dirichlet-Neumann operator | differential | MATHEMATICS | EQUATIONS | WATER-WAVES | WELL-POSEDNESS

Journal Article

Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 10/2017, Volume 147, Issue 5, pp. 895 - 916

In this note semi-bounded self-adjoint extensions of symmetric operators are investigated with the help of the abstract notion of quasi boundary triples and...

Dirichlet-Neumann map | Boundary triple | Weyl function | Elliptic differential operator | Semi-bounded operator | SPECTRAL THEORY | EIGENVALUE | MATHEMATICS, APPLIED | ELLIPTIC DIFFERENTIAL-OPERATORS | LAPLACIAN | MATHEMATICS | boundary triple | RESOLVENT FORMULAS | LARGE PARAMETER | DOMAINS | semi-bounded operator | elliptic differential operator | Operators (mathematics) | Partial differential equations | Differential equations | Dirichlet–Neumann map | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis

Dirichlet-Neumann map | Boundary triple | Weyl function | Elliptic differential operator | Semi-bounded operator | SPECTRAL THEORY | EIGENVALUE | MATHEMATICS, APPLIED | ELLIPTIC DIFFERENTIAL-OPERATORS | LAPLACIAN | MATHEMATICS | boundary triple | RESOLVENT FORMULAS | LARGE PARAMETER | DOMAINS | semi-bounded operator | elliptic differential operator | Operators (mathematics) | Partial differential equations | Differential equations | Dirichlet–Neumann map | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis

Journal Article

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