ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 07/2012, Volume 18, Issue 3, pp. 712 - 747

Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability...

Elliptic operators | Semiclassical analysis | Controllability | Carleman estimates | Observability | Parabolic operators | MATHEMATICS, APPLIED | THEOREM | STABILIZATION | parabolic operators | elliptic operators | SEMILINEAR HEAT-EQUATIONS | controllability | ONE CONTROL FORCE | NAVIER-STOKES | COEFFICIENTS | SYSTEMS | NULL-CONTROLLABILITY | observability | semiclassical analysis | AUTOMATION & CONTROL SYSTEMS | JUMPS | Studies | Mathematical models | Mathematics | Numerical analysis | Partial differential equations | Analysis of PDEs

Elliptic operators | Semiclassical analysis | Controllability | Carleman estimates | Observability | Parabolic operators | MATHEMATICS, APPLIED | THEOREM | STABILIZATION | parabolic operators | elliptic operators | SEMILINEAR HEAT-EQUATIONS | controllability | ONE CONTROL FORCE | NAVIER-STOKES | COEFFICIENTS | SYSTEMS | NULL-CONTROLLABILITY | observability | semiclassical analysis | AUTOMATION & CONTROL SYSTEMS | JUMPS | Studies | Mathematical models | Mathematics | Numerical analysis | Partial differential equations | Analysis of PDEs

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2008, Volume 136, Issue 12, pp. 4245 - 4255

... that by an isoperimetric inequality of Chiti Ch, can be bounded from above in terms of the eigenvalue 1(0). This yields the estimate eq:main0 j (-j(0))+ 2d+2 Hd-1 (1(0))-d/2 (- 1(0...

Electric potential | Ratios | Eigenvalues | Eigenfunctions | Mathematical constants | Mathematical inequalities | Laplacians | Magnetic fields | College mathematics | Laplace operator | Eigenvalue bounds | Semi-classical estimates | Magnetic Schrödinger operator | semi-classical estimates | 1ST 2 EIGENVALUES | MATHEMATICS | MATHEMATICS, APPLIED | DIRICHLET LAPLACIAN | BOUNDS | eigenvalue bounds | magnetic Schrodinger operator | TRACE IDENTITIES | RATIO | POSITIVE POTENTIALS

Electric potential | Ratios | Eigenvalues | Eigenfunctions | Mathematical constants | Mathematical inequalities | Laplacians | Magnetic fields | College mathematics | Laplace operator | Eigenvalue bounds | Semi-classical estimates | Magnetic Schrödinger operator | semi-classical estimates | 1ST 2 EIGENVALUES | MATHEMATICS | MATHEMATICS, APPLIED | DIRICHLET LAPLACIAN | BOUNDS | eigenvalue bounds | magnetic Schrodinger operator | TRACE IDENTITIES | RATIO | POSITIVE POTENTIALS

Journal Article

ASYMPTOTIC ANALYSIS, ISSN 0921-7134, 2009, Volume 65, Issue 3-4, pp. 147 - 174

.... We derive resolvent estimates for semi-classical Schrodinger operator with matrix-valued potential under a geometric condition of the same type on the crossing set and we analyze examples...

semi-classical Schrodinger equation | SCHRODINGER OPERATOR | EIGENVALUES | MATHEMATICS, APPLIED | eigenvalue crossing | Wigner measure | SEMICLASSICAL ANALYSIS | matrix-valued potential | ABSENCE | normal form | RESONANCES | EQUATION

semi-classical Schrodinger equation | SCHRODINGER OPERATOR | EIGENVALUES | MATHEMATICS, APPLIED | eigenvalue crossing | Wigner measure | SEMICLASSICAL ANALYSIS | matrix-valued potential | ABSENCE | normal form | RESONANCES | EQUATION

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 341, Issue 2, pp. 1170 - 1180

We study the semi-classical trace formula at a critical energy level for a Schrödinger operator on R n . We assume here that the potential has a totally...

Schrödinger operators | Trace formula | Semi-classical analysis | MATHEMATICS | Schrodinger operators | MATHEMATICS, APPLIED | semi-classical analysis | trace formula

Schrödinger operators | Trace formula | Semi-classical analysis | MATHEMATICS | Schrodinger operators | MATHEMATICS, APPLIED | semi-classical analysis | trace formula

Journal Article

Asian Journal of Mathematics, ISSN 1093-6106, 2007, Volume 11, Issue 2, pp. 217 - 250

This is a survey paper on the topic of proving or disproving a priori L-2 estimates for non-selfadjoint operators...

Pseudospectrum | Pseudodifferential operators | Solvability | Semi-classical estimates | semi-classical estimates | MATHEMATICS | MATHEMATICS, APPLIED | LOCAL SOLVABILITY | pseudodifferential operators | HARMONIC-OSCILLATOR | PARTIAL DIFFERENTIAL EQUATIONS | CONDITION PSI | PSEUDOSPECTRA | solvability | pseudospectrum | SCHRODINGER-OPERATORS | 47G30 | 35S05 | 47G05

Pseudospectrum | Pseudodifferential operators | Solvability | Semi-classical estimates | semi-classical estimates | MATHEMATICS | MATHEMATICS, APPLIED | LOCAL SOLVABILITY | pseudodifferential operators | HARMONIC-OSCILLATOR | PARTIAL DIFFERENTIAL EQUATIONS | CONDITION PSI | PSEUDOSPECTRA | solvability | pseudospectrum | SCHRODINGER-OPERATORS | 47G30 | 35S05 | 47G05

Journal Article

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, ISSN 1435-9855, 2020, Volume 22, Issue 4, pp. 1003 - 1094

... and Neumann conditions simultaneously. We also prove a resolvent estimate for the generator of the damped plate semigroup associated with these boundary conditions...

MATHEMATICS, APPLIED | stabilization | interpolation inequality | CAUCHY-PROBLEM | spectral inequality | resolvent estimate | UNIQUE CONTINUATION | MATHEMATICS | Carleman estimate | PLATE EQUATION | controllability | 2ND-ORDER ELLIPTIC-EQUATIONS | High-order operators | COEFFICIENTS | boundary value problem | NULL-CONTROLLABILITY | semi-classical calculus | NODAL SETS | JUMPS

MATHEMATICS, APPLIED | stabilization | interpolation inequality | CAUCHY-PROBLEM | spectral inequality | resolvent estimate | UNIQUE CONTINUATION | MATHEMATICS | Carleman estimate | PLATE EQUATION | controllability | 2ND-ORDER ELLIPTIC-EQUATIONS | High-order operators | COEFFICIENTS | boundary value problem | NULL-CONTROLLABILITY | semi-classical calculus | NODAL SETS | JUMPS

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 05/2014, Volume 287, Issue 7, pp. 825 - 835

We prove resolvent estimates for self‐adjoint operators of the form P(h)=−h2Δ+V(x,h) on L2(Rn), n≥3, where 0 35B37 | Potential | 35J15 | resolvent | 47F05 | semi‐classical | Semi-classical | Resolvent | MATHEMATICS | RANGE SCHRODINGER-OPERATORS | BOUNDS | semi-classical | RIEMANNIAN-MANIFOLDS

Journal Article

Asymptotic Analysis, ISSN 0921-7134, 03/2016, Volume 97, Issue 1-2, pp. 61 - 89

...)-estimates for the difference of these and the exact eigenfunctions of the associated Dirichlet-operators.

WKB-expansions | multi-well potential | semi-classical difference operator | tunneling | Agmon estimates | Dirichlet eigenfunctions | asymptotic expansion | MATHEMATICS, APPLIED | METASTABILITY

WKB-expansions | multi-well potential | semi-classical difference operator | tunneling | Agmon estimates | Dirichlet eigenfunctions | asymptotic expansion | MATHEMATICS, APPLIED | METASTABILITY

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2017, Volume 145, Issue 5, pp. 2167 - 2181

As a corollary we obtain lower bounds for the individual eigenvalues \lambda _k, which for a certain range of k improves the Li-Yau inequality for convex...

Berezin–Li–Yau inequality | Semi-classical estimates | Dirichlet-Laplace operator | semi-classical estimates | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | BOUNDS | Berezin-Li-Yau inequality | DIRICHLET

Berezin–Li–Yau inequality | Semi-classical estimates | Dirichlet-Laplace operator | semi-classical estimates | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | BOUNDS | Berezin-Li-Yau inequality | DIRICHLET

Journal Article

Bulletin Brazilian Mathematical Society, ISSN 1678-7544, 11/2004, Volume 35, Issue 3, pp. 333 - 344

We prove uniform semi-classical estimates for the resolvent of the Schrödinger operator h 2Δ g + V (x), 0 < h ≪ 1, at a nontrapping energy level E...

generalized geodesics | 35B37 | Mathematical and Computational Physics | semi-classical resolvent estimates | Mathematics | 35J15 | non-trapping energy level | 47F05 | Generalized geodesics | Non-trapping energy level | Semi-classical resolvent estimates | MATHEMATICS | SINGULARITIES

generalized geodesics | 35B37 | Mathematical and Computational Physics | semi-classical resolvent estimates | Mathematics | 35J15 | non-trapping energy level | 47F05 | Generalized geodesics | Non-trapping energy level | Semi-classical resolvent estimates | MATHEMATICS | SINGULARITIES

Journal Article

Multiscale modeling & simulation, ISSN 1540-3467, 2019, Volume 17, Issue 1, pp. 137 - 166

.... These findings are illustrated numerically by means of an original algorithm, which relies on a discrete approximation of the Steklov-Poincare operator for L-epsilon, and for which error estimates are established...

ENERGY | SINGULAR PERTURBATION | SEMICLASSICAL ANALYSIS | BOUNDARY-VALUE-PROBLEMS | bound states | PHYSICS, MATHEMATICAL | Bessel functions | LOW-LYING EIGENVALUES | spectrum of Schrodinger equation | DIFFERENTIABILITY PROPERTIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SEMI-CLASSICAL LIMIT | FINITE POINT METHOD | DIRICHLET PROBLEM | truly two-dimensional scheme | asymmetric double well potential | error estimates | EQUATION | Mathematics | Mathematical Physics | Numerical Analysis | Analysis of PDEs

ENERGY | SINGULAR PERTURBATION | SEMICLASSICAL ANALYSIS | BOUNDARY-VALUE-PROBLEMS | bound states | PHYSICS, MATHEMATICAL | Bessel functions | LOW-LYING EIGENVALUES | spectrum of Schrodinger equation | DIFFERENTIABILITY PROPERTIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SEMI-CLASSICAL LIMIT | FINITE POINT METHOD | DIRICHLET PROBLEM | truly two-dimensional scheme | asymmetric double well potential | error estimates | EQUATION | Mathematics | Mathematical Physics | Numerical Analysis | Analysis of PDEs

Journal Article

Annales de l'Institut Henri Poincaré. Analyse non linéaire, ISSN 0294-1449, 2017, Volume 34, Issue 7, pp. 1793 - 1836

... of Hölder regularity of the semi-classical Strichartz estimate for the fully nonlinear system...

Water waves | Paracomposition | Cauchy problem | Semi-classical Strichartz estimate | EXISTENCE | MATHEMATICS, APPLIED | SINGULARITIES | EQUATIONS | WELL-POSEDNESS | SURFACE-TENSION | WATER-WAVES | SOBOLEV SPACES | NONSMOOTH COEFFICIENTS | BOUNDARY | OPERATORS

Water waves | Paracomposition | Cauchy problem | Semi-classical Strichartz estimate | EXISTENCE | MATHEMATICS, APPLIED | SINGULARITIES | EQUATIONS | WELL-POSEDNESS | SURFACE-TENSION | WATER-WAVES | SOBOLEV SPACES | NONSMOOTH COEFFICIENTS | BOUNDARY | OPERATORS

Journal Article

13.
Full Text
Predictive methods and semi-classical Equations of State for pure ionic liquids: A review

The Journal of chemical thermodynamics, ISSN 0021-9614, 2019, Volume 130, pp. 47 - 94

•Common predictive methods for the study of properties of pure ionic liquids are reviewed.•In particular, group contributions models, QSPR, ANN and other...

Ionic liquids | Predictive methods | Semi-classical approach | Thermophysical properties | Equations of State | GLASS-TRANSITION TEMPERATURE | THERMODYNAMIC PERTURBATION-THEORY | CHEMISTRY, PHYSICAL | ARTIFICIAL NEURAL-NETWORK | THERMAL-DECOMPOSITION TEMPERATURE | CARBON-DIOXIDE SOLUBILITY | THERMODYNAMICS | STRUCTURE-PROPERTY RELATIONSHIP | GROUP-CONTRIBUTION MODEL | ASSOCIATING FLUID THEORY | 0.1 MPA DENSITY | MOLECULAR-DYNAMICS SIMULATIONS

Ionic liquids | Predictive methods | Semi-classical approach | Thermophysical properties | Equations of State | GLASS-TRANSITION TEMPERATURE | THERMODYNAMIC PERTURBATION-THEORY | CHEMISTRY, PHYSICAL | ARTIFICIAL NEURAL-NETWORK | THERMAL-DECOMPOSITION TEMPERATURE | CARBON-DIOXIDE SOLUBILITY | THERMODYNAMICS | STRUCTURE-PROPERTY RELATIONSHIP | GROUP-CONTRIBUTION MODEL | ASSOCIATING FLUID THEORY | 0.1 MPA DENSITY | MOLECULAR-DYNAMICS SIMULATIONS

Journal Article

14.
Full Text
The ground state energy of the three-dimensional Ginzburg–Landau model in the mixed phase

Journal of Functional Analysis, ISSN 0022-1236, 2011, Volume 261, Issue 11, pp. 3328 - 3344

... ≪ H C 2 , we estimate the ground state energy to leading order as the Ginzburg–Landau parameter tends to infinity.

Ginzburg–Landau functional | Variational methods | Thermodynamic limits | Elliptic estimates | Semi-classical analysis | Ginzburg-Landau functional | MATHEMATICS | SURFACE SUPERCONDUCTIVITY | NUCLEATION | Magnetic fields | Thermodynamics | Analysis

Ginzburg–Landau functional | Variational methods | Thermodynamic limits | Elliptic estimates | Semi-classical analysis | Ginzburg-Landau functional | MATHEMATICS | SURFACE SUPERCONDUCTIVITY | NUCLEATION | Magnetic fields | Thermodynamics | Analysis

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 1998, Volume 48, Issue 4, pp. 1189 - 1229

...). We obtain estimates on the eigenvalues and eigensections of T-k as k --> infinity, in terms of the classical Hamilton flow of H...

Spectral theory | Toeplitz operators | Geometric quantization | Semi-classical analysis | KAHLER-MANIFOLDS | MATHEMATICS | LIMITS | semi-classical analysis | spectral theory | TRACE FORMULA | geometric quantization | QUANTIZATION

Spectral theory | Toeplitz operators | Geometric quantization | Semi-classical analysis | KAHLER-MANIFOLDS | MATHEMATICS | LIMITS | semi-classical analysis | spectral theory | TRACE FORMULA | geometric quantization | QUANTIZATION

Journal Article

Communications in Mathematical Sciences, ISSN 1539-6746, 2016, Volume 14, Issue 8, pp. 2331 - 2371

In this paper, the initial-boundary value problem of a 1-D bipolar quantum semiconductor hydrodynamic model is investigated under a non-linear boundary...

Asymptotic stability | Bipolar quantum hydrodynamic model | Semi-classical limit | Stationary solution | Energy estimates | EXISTENCE | MATHEMATICS, APPLIED | semi-classical limit | DECAY | SEMICONDUCTORS | BEHAVIOR | EQUATIONS | THERMAL-EQUILIBRIUM SOLUTION | EULER-POISSON SYSTEM | asymptotic stability | stationary solution | energy estimates | STEADY-STATE

Asymptotic stability | Bipolar quantum hydrodynamic model | Semi-classical limit | Stationary solution | Energy estimates | EXISTENCE | MATHEMATICS, APPLIED | semi-classical limit | DECAY | SEMICONDUCTORS | BEHAVIOR | EQUATIONS | THERMAL-EQUILIBRIUM SOLUTION | EULER-POISSON SYSTEM | asymptotic stability | stationary solution | energy estimates | STEADY-STATE

Journal Article

2014 International Conference on Computational Science and Computational Intelligence, 03/2014, Volume 1, pp. 360 - 363

We adapt the classical proof of Wentzel-Freidlin estimates for jump processes to the case of an operator of order four...

Geometry | Context | Presses | Upper bound | Semi-classical analysis. Large deviations. Operator of order four | Generators | Standards | Equations | Operator of order four | Semi-classical analysis | Large deviations | Operators | Intelligence | Conferences | Computation | Asymptotic properties | Rescaling | Deviation | Estimates

Geometry | Context | Presses | Upper bound | Semi-classical analysis. Large deviations. Operator of order four | Generators | Standards | Equations | Operator of order four | Semi-classical analysis | Large deviations | Operators | Intelligence | Conferences | Computation | Asymptotic properties | Rescaling | Deviation | Estimates

Conference Proceeding

Annals of Global Analysis and Geometry, ISSN 0232-704X, 10/2004, Volume 26, Issue 3, pp. 271 - 313

...Annals of Global Analysis and Geometry 26: 271–313, 2004. C null 2004 Kluwer Academic Publishers. Printed in the Netherlands. 271 Asymptotic Estimates for a V...

Geometry | semi-classical limits | p -Laplacian | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Mathematical and Computational Physics | first eigenvalue | Mathematics | Group Theory and Generalizations | nonlinear equation | tunelling effect | p-Laplacian | MATHEMATICS | EQUATIONS | Studies | Eigen values

Geometry | semi-classical limits | p -Laplacian | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Mathematical and Computational Physics | first eigenvalue | Mathematics | Group Theory and Generalizations | nonlinear equation | tunelling effect | p-Laplacian | MATHEMATICS | EQUATIONS | Studies | Eigen values

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 4/2012, Volume 63, Issue 2, pp. 203 - 231

We study the eigenpairs of a model Schrödinger operator with a quadratic potential and Neumann boundary conditions on a half-plane. The potential is degenerate...

65N25 | Primary 99Z99 | Born-Oppenheimer approximation | 41A60 | 35P20 | Theoretical and Applied Mechanics | Engineering | Mathematical Methods in Physics | Secondary 00A00 | 35P15 | Schrödinger operator | Agmon estimates | 65N30 | Semi classical limit | LAPLACIAN | MATHEMATICS, APPLIED | SUPERCONDUCTIVITY | 3-DIMENSIONS | Schrodinger operator | VARIABLE MAGNETIC-FIELD | Mathematics | Mathematical Physics | Analysis of PDEs | Physics

65N25 | Primary 99Z99 | Born-Oppenheimer approximation | 41A60 | 35P20 | Theoretical and Applied Mechanics | Engineering | Mathematical Methods in Physics | Secondary 00A00 | 35P15 | Schrödinger operator | Agmon estimates | 65N30 | Semi classical limit | LAPLACIAN | MATHEMATICS, APPLIED | SUPERCONDUCTIVITY | 3-DIMENSIONS | Schrodinger operator | VARIABLE MAGNETIC-FIELD | Mathematics | Mathematical Physics | Analysis of PDEs | Physics

Journal Article

Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 01/1999, Volume 455, Issue 1981, pp. 183 - 217

... for Pauli and−Eigenvalue estimates in the semi Email alerting service herecorner of the article or click Receive free email alerts when new articles cite this article...

Spectral theory | Eigenvalues | Mathematical inequalities | Mathematical vectors | Eigenvectors | Magnetic fields | Operator theory | Perceptron convergence procedure | College mathematics | Semi-classical asymptotics | Eigenvalues and essential spectrum | Coherent state analysis | Essential self-adjointness | Pauli and dirac operators | MATTER | THOMAS-FERMI | Pauli and Dirac operators | MULTIDISCIPLINARY SCIENCES | coherent state analysis | ATOMS | eigenvalues and essential spectrum | semi-classical asymptotics | essential self-adjointness | SCHRODINGER-OPERATORS

Spectral theory | Eigenvalues | Mathematical inequalities | Mathematical vectors | Eigenvectors | Magnetic fields | Operator theory | Perceptron convergence procedure | College mathematics | Semi-classical asymptotics | Eigenvalues and essential spectrum | Coherent state analysis | Essential self-adjointness | Pauli and dirac operators | MATTER | THOMAS-FERMI | Pauli and Dirac operators | MULTIDISCIPLINARY SCIENCES | coherent state analysis | ATOMS | eigenvalues and essential spectrum | semi-classical asymptotics | essential self-adjointness | SCHRODINGER-OPERATORS

Journal Article

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