Wednesday , 19 December 2018
«Les savants des temps passés et des nations révolues n’ont cessé
de composer des livres. Ils l’ont fait pour léguer leur savoir à ceux
qui les suivent. Ainsi demeurera vive la quête de la vérité.»

[ Al-Khwarizmi ]


Guest Editor of a special Issue in Applicable Analysis:

New Trends in PDEs and Applications
Home » Publications

Publications

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). PDF format
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). PDF format
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).PDF format
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).PDF format
5- Cases of equality and strict inequality in the extended Hardy-Littlewood inequalities, Proc. Royal. Soc. Edinburgh, 135 A, (2005), 643-661. PDF format
6- Extended Hardy-Littlewood inequalities and some applications, Trans. Amer. Math. Soc., vol. 357, no. 12, (2005) pp. 4885-4896. PDF format
7- Rearrangement inequalities for functionals with monotone integrals, Journal of Functional Analysis, 233, (2006), 561-582. (with A. Burchard). PDF format
8- Uniqueness and Characterization of the maximizers of some integral functionals, Adv Nonlinear Studies 9, (2009), 215-226. (with C. Draghici). PDF format
9- Symmetric ground states solutions of m-coupled nonlinear Schrödinger equations, Nonlinear Analysis: Methods, Theory and Applications, Vol 71, 2, (2009). PDF format
10- Explicit approximation to symmetrization via iterated polarizations, Journal of Convex Analysis, Vol 17, N2, (2010).pdf
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.pdf
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. PDF format
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. PDF format
15- On Schrödinger Systems Arising in Nonlinear Optics And Quantum Mechanics – Part I, MA3S,
vol 22, issue 7, 1-27, 2012.
PDF format
16- On Schrödinger Systems Arising in Nonlinear Optics And Quantum Mechanics – Part II, Nonlinearity 26, Number 4, 2013. PDF format
17- Quantitative stability estimates of the Hardy-Littlewood functional under constraints, Journal of Nonlinear and Convex Analysis, Vol. 13, number 2, 273-279, 2012. PDF format
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. PDF format
20- Characterization of maximizers via mass transportation techniques, Journal of Optimization Theory and Applications. Vol. 155, N 2, November2012. PDF format
21- Orbital stability of l-Coupled nonlinear Schrodinger equations,Communications in Contemporary Mathematics, Volume 14, Issue 06, December 2012. PDF format
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). PDF format
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. PDF format
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. PDF format
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). PDF format
26- Characterization of the orbit of Standing waves of Hartree type equations with external Coulomb Potential, Asymtotic Analysis,
87 (2014) 57-64.
PDF format
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) PDF format
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). PDF format
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)..
PDF format
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). PDF format
31- Symmetry of minimizers of some fractional problems, Accepted in Applicable Analysis.pdf
32- Orbital Stability of Standing Waves of Two-Component Bose-Einstein condensates with internal Atomic Josephson Junnction. Accepted in Journal of
Mathematical Analysis and Applicationspdf
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).pdf
34- Sharp embedding of Sobolev Spaces Involving General kernels and its application Accepted in Annales Henri Poincaré.pdf
35- On the global Cauchy problem for non-linear Schrodinger equation with magnetic potential, Preprint (with N Boussaid, S. Ibrahim, L. Michel).pdf
36- On a new class of functional problems, Preprint.pdf
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 Ipdf
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.pdf
41- Existence, Uniqueness and Non-Existence of solutions for semilinear Elliptic equation involving measures concentrated on the boundaries, Preprint (with H.Chen).pdf
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).pdf
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).pdf
44- Complementary study of the standing wave solutions of the Gross-Pitaevskii equation in dipolar quantum gases (with R. Carles).pdf
45- On a class of semilinear fractional elliptic equations involving outside Dirac data ( with H. Chen and Y. Wang).pdf
46- Existence, Non-existence, Uniqueness of solutions for semilinear elliptic equations involving measures concentrated on boundary ( with H. Chen)pdf
47- Boundary blow-up solutions to fractional elliptic equations in a measure framework ( with H. Chen and Y. Wang).pdf

Ph.D. dissertation:

Inégalités de symétrisation et applications, EPFL, Lausanne (advisor: C.A. Stuart). PDF format

 

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