Hajaiej Hichem
My Articles :
The Mathematical Explanation of the Crash of Malaysia Airlines Flight MH 370 (In preparation)
1- Symmetrization inequalities for composition operators of Carathéodory type,Proc. London. Math. Soc., 87(2003), 396-418. (with C. A. Stuart).  |
| 2- Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization,International Journal of Mathematics and Mathematical Sciences, 59(2004), 3129-3150. (with C. A. Stuart). |
| 3- Existence and non-existence of Schwarz symmetric ground states for elliptic eigenvalue problems, Annali de Matematica Pura ed Applicata, Volume 184, Number 3, (2005), 297 -314. (with C.A.Stuart). |
| 4- On the variational approach to the stability of standing waves for the nonlinear Schrödinger equation, Adv Nonlinear Studies, 4 (2004), 469-501. (with C.A Stuart). |
| 5- Cases of equality and strict inequality in the extended Hardy-Littlewood inequalities, Proc. Royal. Soc. Edinburgh, 135 A, (2005), 643-661. |
| 6- Extended Hardy-Littlewood inequalities and some applications, Trans. Amer. Math. Soc., vol. 357, no. 12, (2005) pp. 4885-4896. |
| 7- Rearrangement inequalities for functionals with monotone integrals, Journal of Functional Analysis, 233, (2006), 561-582. (with A. Burchard). |
| 8- Uniqueness and Characterization of the maximizers of some integral functionals, Adv Nonlinear Studies 9, (2009), 215-226. (with C. Draghici). |
| 9- Symmetric ground states solutions of m-coupled nonlinear Schrödinger equations, Nonlinear Analysis: Methods, Theory and Applications, Vol 71, 2, (2009). |
| 10- Explicit approximation to symmetrization via iterated polarizations, Journal of Convex Analysis, Vol 17, N2, (2010). |
| 11- Balls are the maximizers of the Riesz type integrals with supermodular integrands, Annali de Matematica Pura ed Applicata, Volume 189, Issue 3 (2010), 395-403. |
| 12- Rearrangement Inequalities in the Discrete setting and some Applications,Nonlinear Analysis: Theory Methods and Applications 59 (2010), 1140-1148. |
| 13- On the necessity of the assumptions used to prove generalized Hardy-Littlewood and Riesz type rearrangement inequalities, Archiv der Matematik vol 96, Number 3, 273-280, 2011. |
| 14- Fractional Gagliardo-Nirenberg and Hardy Inequalities under Lorentz Norms.Accepted for publication in Journal of Mathematical Analysis and Applications. (with Z. Zhichcun and X. Yu), J. Math. Anal. Appl. 396(2), 569-577 2012. |
| 15- On Schrödinger Systems Arising in Nonlinear Optics And Quantum Mechanics – Part I, MA3S, vol 22, issue 7, 1-27, 2012. |
| 16- On Schrödinger Systems Arising in Nonlinear Optics And Quantum Mechanics – Part II, Nonlinearity 26, Number 4, 2013. |
| 17- Quantitative stability estimates of the Hardy-Littlewood functional under constraints, Journal of Nonlinear and Convex Analysis, Vol. 13, number 2, 273-279, 2012. |
| 18- A weak-strong convergence property and symmetry of minimizers of constrained variational problems in RN. Journal of Mathematical Analysis and Application. Vol 389, Number 2 915-931, 2012. (with S. Kroemer). |
| 19- Existence and uniqueness of maximizers of a class of functionals under constraints: Optimal conditions. Journal of Inequalities and Applications 2012 Issue 1. |
| 20- Characterization of maximizers via mass transportation techniques, Journal of Optimization Theory and Applications. Vol. 155, N 2, November2012. |
| 21- Orbital stability of l-Coupled nonlinear Schrodinger equations,Communications in Contemporary Mathematics, Volume 14, Issue 06, December 2012. |
| 22- Necessary and sufficient conditions for the fractional Gargliardo-Nirenberg inequalities and applications to Navier-Stokes and generalized boson equations,RIMS Kokyuroku Bessatsu, B26 (2011), 159-199. (with L. Molinet, T. Ozawa, B. Wang). |
| 23- Existence of minimizers of functional involving the fractional gradient in the absence of compactness, symmetry and monotonicit, Journal of Mathematical Analysis and Applications, Vol. 399, No. 1. (March 2013), pp. 17-26. |
| 24- On the optimality of the conditions used to prove the symmetry of the minimizers of some fractional constrained variational problems, Annales de l’Institut Henri Poincare, Volume 14, Issue 5 (2013), Pages 1425-1433. |
| 25- On the Cauchy problem of fractional Schrodinger equation with hartree type nonlinearity, Funkcialaj Ekvacioj of volume 56 no 2 2013, p. 193-224. (with Y. Cho, G. Hwang and T. Ozawa). |
| 26- Characterization of the orbit of Standing waves of Hartree type equations with external Coulomb Potential, Asymtotic Analysis, 87 (2014) 57-64. |
| 27- On the Xfel Schr¨odinger equation: Highly oscillatory magnetic potentials and time averaging, Archive for Rational Mechanics and Analysis, Volume 211, Issue 3, pp 711-732 (2014), ( with P. Antonelli, A. Athanoulissis and P. Markowich) |
| 28- On the orbital stability of fractional Schrödinger equations, accepted in Communications in Pure and Applied Anlysis (CPAA), (with Y. Cho, G. Hwang and T. Ozawa). |
| 29- Multi-Configuration Hartree Fock Theory for Pseudorelativistic systems: The Time Dependent Case, Vol 24, N 3 (2014), 599-626, Mathematical Models and Methods in Applied Sciences (with S. Trabelsi and P. Markowich).. |
| 30- Existence of Minimizers of a Class of Constrained Vectorial Variational Problems, Milan Journal of Mathematics, Volume 82, Issue 1(2014) Page 81-98. (with S. Trabelsi, P. Markowich). |
| 31- Symmetry of minimizers of some fractional problems, Accepted in Applicable Analysis. |
| 32- Orbital Stability of Standing Waves of Two-Component Bose-Einstein condensates with internal Atomic Josephson Junnction. Accepted in Journal of Mathematical Analysis and Applications |
| 33- Variational Appraoch to the orbital Stability of Standing Waves in Bose-Einstein Condensates, Accepted in Milan Journal of Mathematics (with F. Hadj Selem, P Markowich S. Trabelsi). |
| 34- Sharp embedding of Sobolev Spaces Involving General kernels and its application Accepted in Annales Henri Poincaré. |
| 35- On the global Cauchy problem for non-linear Schrodinger equation with magnetic potential, Preprint (with N Boussaid, S. Ibrahim, L. Michel). |
| 36- On a new class of functional problems, Preprint. |
| 37- Existence of Minimizers of a Class of Constrained Vectorial Variational Problems, Part 2, Preprint. (with P . Markowich, S. Trabelsi). |
| 38- A complete study of the lack of compactness and existence results of a Fractional Nirenberg Equation via a flatness hypothesis: Part I |
| 39- A complete study of the lack of compactness and existence results of a Fractional Nirenberg Equation via a flatness hypothesis: Part II |
| 40- On the spin of Bose Einstein condensate in the presence of Ioffe-Pritchard Magnetic field, Preprint. |
| 41- Existence, Uniqueness and Non-Existence of solutions for semilinear Elliptic equation involving measures concentrated on the boundaries, Preprint (with H.Chen). |
| 42- Open FOAM computation of interacting wind turbine flows and control (I): free rotating case, Preprint (with G. Chen C. Gu, Philip J. Morris, Eric G. Paterson, A. Sergeev). |
| 43- Orbital stability of standing waves of a class of fractional Schr¨odinger equations with general Hartree-type integrand, Preprint (with Y Cho, M.M Fall, S. Trabelsi, P. Markowich). |
| 44- Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases (with R. Carles). |
| 45- On a class of semilinear fractional elliptic equations involving outside Dirac data ( with H. Chen and Y. Wang). |
| 46- Existence, Non-existence, Uniqueness of solutions for semilinear elliptic equations involving measures concentrated on boundary ( with H. Chen) |
| 47- Boundary blow-up solutions to fractional elliptic equations in a measure framework ( with H. Chen and Y. Wang). |
Ph.D. dissertation:
Inégalités de symétrisation et applications, EPFL, Lausanne (advisor: C.A. Stuart).