Semiclassical resonances in some simple cases
Semiclassical scattering by the Coulomb potential
Semi-classical trace formula and clustering of eigenvalues for Schrödinger operators
Semilinear elliptic problems on unbounded subsets of the Heisenberg group.
Sharp estimates for singular transport equations
We provide estimates for a transport equation which contains singular integral operators. The form of the equation was motivated by the study of Kirchhoff–Sobolev parametrices in a Lorentzian space-time satisfying the Einstein equations. While our main application is for a specific problem in General Relativity we believe that the phenomenon which our result illustrates is of a more general interest.
Sharp polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in IRn.
Ski de fond
Smoothing effect for regularized Schrödinger equation on compact manifolds
Smoothing effect for Schrödinger evolution equation via commutator algebra
Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics
Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.The object of this article is to present the computational solution of one-dimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function. It provides an elegant...
Solution of the Neumann problem for the Laplace equation
For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.
Solutions of boundary-value problems in discretized volumes.
Solutions to stationary phase-field equations.
Solvability Conditions for a Linearized Cahn-Hilliard Equation of Sixth Order
We obtain solvability conditions in H6(ℝ3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results derived for a Schrödinger type operator without Fredholm property in our preceding article [18].
Some estimates concerning the Zeeman effect
The Itô integral calculus and analysis on nilpotent Lie grops are used to estimate the number of eigenvalues of the Schrödinger operator for a quantum system with a polynomial magnetic vector potential. An analogue of the Cwikel-Lieb-Rosenblum inequality is proved.
Some estimates for commutators of Riesz transform associated with Schrödinger type operators
Let be a Schrödinger operator and let be a Schrödinger type operator on , where is a nonnegative potential belonging to certain reverse Hölder class...
Some estimates of Schrödinger-type operators with certain nonnegative potentials.
Some mathematical problems in inverse potential scattering
Some problems in inverse scattering theory
Some remarks on double-wells in one and three dimensions