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ESAIM: Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 3/2012, Volume 18, Issue 3, pp. 712 - 747
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, 2009, Volume 65, Issue 3-4, pp. 147 - 174
In this article, we analyze the propagation of Wigner measures of a family of solutions to a system of semi-classical pseudodifferential equations presenting... 
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
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2006, Volume 226, Issue 1, pp. 295 - 322
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... 
Degenerate oscillatory integrals | Schrödinger operators | Trace formula | Semi-classical analysis | MATHEMATICS | Schrodinger operators | semi-classical analysis | degenerate oscillatory integrals | trace formula | Mathematics | Spectral Theory | Classical Physics | Analysis of PDEs | Physics
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. Our framework will be limited to the case of... 
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
Journal Article
Asymptotic Analysis, ISSN 0921-7134, 03/2016, Volume 97, Issue 1-2, pp. 61 - 89
We analyze a general class of difference operators H-epsilon = T-epsilon + V-epsilon on l(2)(((epsilon)Z)(d)), where V-epsilon is a multi-well potential and... 
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 | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis
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 > 0, where V... 
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 1540-3459, 2019, Volume 17, Issue 1, pp. 137 - 166
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 12/2017, Volume 34, Issue 7, pp. 1793 - 1836
This article is devoted to the Cauchy problem for the 2D gravity-capillary water waves in fluid domains with general bottoms. Local well-posedness for this... 
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
The Journal of Chemical Thermodynamics, ISSN 0021-9614, 01/2019, Volume 130, pp. 47 - 94
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2011, Volume 261, Issue 11, pp. 3328 - 3344
We consider the Ginzburg–Landau functional defined over a bounded and smooth three-dimensional domain. Supposing that the strength of the applied magnetic... 
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
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
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 1998, Volume 48, Issue 4, pp. 1189 - 1229
Let X be compact Kahler manifold with integral Kahler class and L --> X a holomorphic Hermitian line bundle whose curvature is the symplectic form of X. Let H... 
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
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. The different rescaling for the... 
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
Let Ω be a domain of ℝ N . We study the infimum λ1(h) of the functional ∫Ω|∇u| p +h −p V(x)|u| p dx in W 1,p (Ω) for ||u|| LP(Ω)= 1 where h > 0 tends to zero... 
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
Journal Article
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