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Nassif Ghoussoub

List of Research Papers

Books and Memoirs

  1. N. Ghoussoub, B. Maurey: Hδ-embeddings in Hilbert space and Optimization on Gδ-sets, Memoirs of the A.M.S., No. 349 (1986) 102 pp
  2. N. Ghoussoub, G. Godefroy, B. Maurey, W. Schachermayer: Some Topological and Geometrical Structures in Banach Spaces, Memoire A.M.S., Vol. 70, No. 378 (1987) 120 pp
  3. N. Ghoussoub: Duality and Perturbation Methods in Critical Point Theory. Research Monograph, Cambridge Tracts, Cambridge University Press (1993) 268 pp
  4. N. Ghoussoub, F. Robert: Concentration estimates for Emden-Fowler Equations with boundary singularities and critical growth, International Mathematics Research Papers (2006) 86 pp
  5. N. Ghoussoub: Self-dual Partial Differential Systems and Their Variational Principles, Springer Monographs in Mathematics, Springer New York (2008) 354
  6. P. Esposito, N. Ghoussoub, Y. Guo: Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS, Courant Lecture Notes, In press (2009) 332 pp (revised October 23, 2009)
  7. N. Ghoussoub: Dentability, balayage and optimization on non-compact manifolds. Research Monograph, In preparation
  8. N. Ghoussoub: Morse theory up to epsilon: Theory and Applications, In preparation

Research Papers

  1. C. Cowan, P. Esposito, N. Ghoussoub: Regularity of Extremal Solutions in Fourth Order Nonlinear Eigenvalue Problems on General Domains, Discrete and Continuous Dynamical Systems - Series A, Vol 28, 3 (2010) p. 1033-1050
  2. N. Ghoussoub, A. Moameni, R. Saiz: Homogenization of maximal monotone vector fields via selfdual variational calculus, Submitted (2010) 30 pp
  3. N. Ghoussoub, C.S. Lin: On the best constant in the Moser-Onofri-Aubin inequality on S2, Comm. in Math. Physics, In press (2010) 10 pp
  4. C. Cowan, N. Ghoussoub: Estimates on Pull-In Distances in Microelectromechanical Systems Models and Other Nonlinear Eigenvalue Problems, SIAM Journal on Mathematical Analysis, Vol. 42, No. 5 (2010) p. 1949-1966
  5. C. Cowan, P. Esposito, N. Ghoussoub, A. Mordifam: The critical dimension for a fourth order elliptical problem with singular nonlinearity, Arch. Ration. Mech. Anal., In press (2009) 19 pp
  6. C. Cowan, N. Ghoussoub: Regularity of the extremal solution in a MEMS model with advection, Methods and Applications of Analysis, Vol. 15, No 3 (2008) p. 355-362
  7. P. Esposito, N. Ghoussoub: Uniqueness of solutions for an elliptic equation modeling MEMS, Methods and Applications of Analysis, Vol. 15, No 3 (2008) pp. 341-354
  8. D. Cassani, J. M. do O, N. Ghoussoub: On a fourth order elliptic problem with a singular nonlinearity, Journal of Advanced Nonlinear Studies, Vol. 9 (2009) p. 177-197
  9. N. Ghoussoub: A variational theory for monotone vector fields, Journal of Fixed Point Theory and Applications, Vol. 4 Number 1 (2008) p. 107-135
  10. N. Ghoussoub: Hamiltonian systems as selfdual equations, Frontiers of Mathematics in China, Vol. 3, Number 2 (2008) p. 167-193
  11. N. Ghoussoub, A. Moradifam: Bessel pairs and optimal Hardy-Rellich Inequalities, Math. Annalen, Published Online (March 26, 2010) 57 pp
  12. N. Ghoussoub, Y. J. Guo: Estimates for the quenching time of a parabolic equation modeling electrostatic MEMS,Methods and Applications of Analysis, Vol. 15, No 3 (2008) p. 361-376
  13. N. Ghoussoub, A. Moradifam: Simultaneous preconditioning and symmetrization of non-symmetric linear systems, Numerical Linear Algebra with Applications, Accepted (March 2010) 6 pp
  14. N. Ghoussoub: Self-dual Partial Differential Systems and Their Variational Principles, Springer Monographs in Mathematics, Springer New York (2008) 356 pp
  15. N. Ghoussoub, A. Moameni: Hamiltonian systems of PDEs with selfdual boundary conditions, Calculus of Variations and PDEs, Vol. 36, No 1 (2009) p. 85-118
  16. N. Ghoussoub, A. Moradifam: On the best possible remaining term in the improved Hardy inequality, Proc. of the Nat. Acad. of Sciences, September 16, 2008 vol. 105 no. 37 13746-13751
  17. P. Esposito, N. Ghoussoub, Y. J. Guo: Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS, Courant Lecture Notes, In press (2009) 332 pp (revised October 23, 2009)
  18. N. Ghoussoub: Superposition of selfdual functionals for non-homogeneous boundary value problems and differential systems, Journal of Discrete and Continuous Dynamical Systems, Vol. 21, 1 (2008), p. 187-220
  19. N. Ghoussoub, A. Moameni: Anti-symmetric Hamiltonians (II): Variational resolution of Navier-Stokes equations and other nonlinear evolutions, Annales de l'Institut Henri Poincaré / Analyse non linéaire 26 (2009), pp. 223-255
  20. N. Ghoussoub, Y. J. Guo: On the Partial Differential Equations of Electrostatic MEMS Devices II: Dynamic Case, Nonlinear Differential Equations and Applications, Vol. 15, No. 1-2 (2008) p. 115-145
  21. P. Esposito, N. Ghoussoub, Y. J. Guo: Compactness along the branch of semi-stable and unstable solutions for an elliptic problem with a singular nonlinearity, Comm. Pure & Applied Math., Vol. 60, No. 12 (2007) p. 1731-1768
  22. N. Ghoussoub, Y. J. Guo: On the Partial Differential Equations of Electrostatic MEMS Devices: Stationary Case, SIAM J. Math. Anal., Vol. 38, No. 5, (2007) p. 1423-1449
  23. N. Ghoussoub, A. Moameni: Selfdual variational principles for periodic solutions of Hamiltonian and other dynamical systems, Comm. in PDE, Vol. 32, No. 5 (2007) p. 771-795
  24. N. Ghoussoub, A. Moameni: On the existence of Hamiltonian paths connecting Lagrangian submanifolds, C.R. Math. Rep. Acad. Sci. Canada Vol. 30, No. 3 (2008) p. 65-83
  25. N. Ghoussoub, F. Robert: Elliptic equations with critical growth and large sets of boundary singularities, Trans. Amer. Math. Soc. 361 (2009), p. 4843-4870
  26. N. Ghoussoub, L. Tzou: Iterations of Anti-selfdual Lagrangians, Hamiltonian systems and multiparameter gradient flows, Calculus of Variations and PDEs, Vol. 26, No. 4 (2006) p. 511-534
  27. N. Ghoussoub, F. Robert: Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth, International Mathematics Research Papers (2006) p. 1-86
  28. N. Ghoussoub, L. Tzou: Anti-selfdual Lagrangians II: Unbounded non self-adjoint operators and evolution equations, Annali di Matematica pura ed Applicata, Vol. 187, No. 2 (2008) p. 323-352
  29. N. Ghoussoub: Anti-symmetric Hamiltonians: Variational resolution of Navier-Stokes equations and other nonlinear evolutions, Comm. Pure & Applied Math., Vol. 60, No. 5 (2007) p. 619-653
  30. N. Ghoussoub: Anti-selfdual Lagrangians: Variational resolutions of non self-adjoint equations and dissipative evolutions, AIHP-Analyse non linéaire, Vol. 24, No. 2 (2007) p. 171-205
  31. N. Ghoussoub, F. Robert: The effect of curvature on the best constant in the Hardy- Sobolev inequalities, Geom. And Funct. Anal. Vol. 16, No. 6 (2006) p. 1201-1245
  32. N. Ghoussoub, Yujin Guo: Dynamic Deflection of Electrostatic MEMS, 2005 International Conference on MEMS, NANO and Smart Systems (2005) p. 341-345
  33. N. Ghoussoub: A theory of Anti-selfdual Lagrangians: Dynamic case, C.R. Acad. Sci., Paris, Vol. 340, No. 4 (2005) p. 325-330
  34. N. Ghoussoub: A theory of Anti-selfdual Lagrangians: Stationary case, C.R. Acad. Sci., Paris, Vol. 340, No. 3 (2005) p. 245-250
  35. 20. N. Ghoussoub: A variational principle for non-linear transport equations, Communications on Pure and Applied Analysis, Vol. 4, No. 4 (2005) p. 735-742
  36. N. Ghoussoub, R. McCann: A least action principle for steepest descent in a non-convex landscape, Contemporary Math. Vol. 362 (2004) p. 177-187
  37. N. Ghoussoub, X.S. Kang: Hardy-Sobolev Critical Elliptic Equations with Boundary Singularities, AIHP-Analyse non linéaire, Vol. 21, No. 6 (2004) p. 767-793
  38. N. Ghoussoub, L. Tzou: A variational principle for gradient flows, Math. Annalen, Vol. 330, No. 3 (2004) p. 519-549
  39. M. Agueh, N. Ghoussoub, X. S. Kang: Geometric inequalities via a general comparison principle for interacting gases, Geom. And Funct. Anal., Vol. 14, No. 1 (2004) p. 215-244
  40. M. Agueh, N. Ghoussoub, X. S. Kang: L'évolution de l'énergie totale d'un gaz le long d'un transport optimal et ses applications, C. R. Acad. des Sci. (2003) p. 173-178
  41. N. Ghoussoub, C. Gui: On the De Giorgi conjecture in dimensions 4 and 5, Annals of Mathematics, Vol. 157 (2003) p. 313-334
  42. I. Ekeland, N. Ghoussoub: Selected new aspects of the calculus of variations in the large, Bulletin (New Series) of the American Mathematical Society, Vol. 39, No. 2 (2002), p. 207-265
  43. C. Chambers, N. Ghoussoub: Perturbations from symmetry and non-homogeneous boundary value problems, Journal of Discrete and Continuous Dynamical Systems, Vol 8, No. 1, (2002) p. 267-281
  44. N. Ghoussoub, C. Gui, M. Zhu: On a singularly perturbed Neumann problem with the critical exponent, Communications in Partial Differential Equations, Vol. 26, No. 11 (2002) p. 1929-1946
  45. R. Deville, N. Ghoussoub: Perturbed Minimization Principles and Applications, Handbook on the Geometry of Banach Spaces, North Holland-Elsevier, Chapter 10 (2001), p. 393-435
  46. N. Ghoussoub, C. Yuan: Multiple Solutions for Quasi-linear PDEs Involving the Critical Sobolev and Hardy Exponents, T.A.M.S, Vol. 352, No. 12 (2000) p. 5703-5743
  47. P. Bolle, N. Ghoussoub, H. Tehrani: The Multiplicity of solutions for non-homogeneous boundary value problems, Manuscripta Math., Vol. 101, No. 3 (2000) p. 325-350
  48. N. Ghoussoub, C. Gui: On a conjecture of De Giorgi and related problems, Math. Annalen, Vol. 311, No. 3 (1998) p. 481-491
  49. J. Feldman, R. Froese, N. Ghoussoub, C. Gui: An improved Moser-Aubin-Onofri inequality for axially symmetric functions on S2, Calculus of Variations and PDE, Vol. 6, No. 2 (1998) p. 95-104
  50. I. Ekeland, N. Ghoussoub: Z2-Equivariant Ljusternik-Schnirelmann Theory for non-even functionals, Annales de l'Institut Henri Poincaré, Analyse non linéaire, Vol. 15, No. 3 (1998) p. 341-370
  51. N. Ghoussoub, C. Gui: Multi-peak solutions for a semi-linear Neuman problem involving the critical Sobolev exponent, Math. Zeitschrift, Vol. 229, No. 3 (1998) p. 443-474
  52. N. Ghoussoub, C. Gui: New variational methods with applications to semilinear Neumann problems involving the critical Sobolev exponent, Special volume for the 50th anniversary of the CMS. Invited papers (1996) p. 125-152
  53. I. Ekeland, N. Ghoussoub, H. Tehrani: Multiple Solutions for a Classical Problem in the Calculus of Variations, Journal of Differential Equation, Vol. 131, No. 2 (1996) p. 229-243
  54. K. C. Chang, N. Ghoussoub: The Conley Index and the Critical Groups via an extension of Gromoll-Meyer theory, Topological Methods in Nonlinear Analysis, Vol. 7, No. 1 (1996) p. 77-93
  55. N. Ghoussoub: A note on the multiplicity of surfaces with prescribed constant mean curvature, CMS seminar on Partial Differential equations, Publications du CRM (1996/97) p. 135-144.
  56. G. Fang, N. Ghoussoub: Morse-type information on Palais-Smale sequences obtained by Min-Max principles. Comm. Pure. Applied. Math., Vol. 47, No. 12 (1994) p. 1595-1653.
  57. N. Ghoussoub: Duality and Perturbation Methods in Critical Point Theory. Research Monograph. Cambridge Tracts of Math. Cambridge University Press (1993) 265 pp
  58. N. Ghoussoub: A Min-Max principle with a relaxed boundary condition. Proc. A.M.S., Vol. 117, No. 2 (1993) p. 439-447.
  59. G. Fang, N. Ghoussoub: Second order information on Palais-Smale sequences in the Mountain Pass Theorem, Manuscripta Math., Vol. 75, No. 2 (1992) p. 81-95
  60. N. Ghoussoub, B. Maurey, W. Schachermayer: Slicings, selections and their applications, Canadian J. Math. 44.3. (1992) p. 483-504
  61. N. Ghoussoub: Location, Multiplicity and Morse Indices of Min-Max Critical Points. J. Reine Angew. Math 417 (1991) p. 27-76
  62. N. Ghoussoub, W.B.Johnson: Operators which factor through Banach lattices not containing c0. Lecture Notes in Mathematics, Springer-Verlag 1470 (1991) p. 68-71
  63. N. Ghoussoub, B. Maurey, W. Schachermayer: Geometrical implications of certain infinite dimensional decompositions, Trans. A.M.S., Vol. 317, No. 2 (1990) p. 541-584
  64. N. Ghoussoub, B. Maurey, W. Schachermayer: Remarks about the interpolation of Radon-Nikodym operators. Lecture Note series, London Math Society, 158 (1990) p. 111-119
  65. N. Ghoussoub, B. Maurey: A non-linear method for constructing certain basic sequences in Banach spaces. Illinois J. Math, Vol. 34, No. 3 (1990) p. 607-613
  66. W. Davis, N. Ghoussoub, W. B. Johnson, Kwapien, B. Maurey: Weak convergence of vector valued martingales. Proc. of the 6th Conference on Probability in Banach spaces - Sonderborg, Denmark. Springer-Verlag (1989). A compendium by P. Orno.
  67. N. Ghoussoub, J. Lindenstrauss, B. Maurey: Analytic martingales and plurisubharmonic barriers in complex Banach spaces. Contemporary Math. Vol. 85 (1989) p. 111-130
  68. N. Ghoussoub, B. Maurey, W. Schachermayer: Pluriharmonically dentable complex Banach spaces. J. reine angew. Math. Band 402 (1989) p. 76-127
  69. N. Ghoussoub, D. Preiss: A General Mountain Pass Principle for locating and classifying critical points. A.I.H.P. Analyse non linéaire, 5, Vol. 6 (1989) p. 321-330
  70. N. Ghoussoub, B. Maurey: Plurisubharmonic martingales and barriers in complex quasi- Banach spaces. Annales Inst. Fourier, Tome 39-Fasc 4 (1989) p. 1007-1060
  71. N. Ghoussoub, B. Maurey: Gδ-embeddings in Hilbert space II, J. Funct. Analysis, Vol. 78, No. 2 (1988) p. 271-305
  72. N. Ghoussoub, W. B. Johnson: Factoring operators through Banach lattices not containing C[0, 1], Math Zeitsch. 194 (l987) p. l53-l7l
  73. N. Ghoussoub, G. Godefroy, B. Maurey, W. Schachermayer: Some Topological and Geometrical Structures in Banach Spaces, Memoire A.M.S., Vol. 70, No. 378 (1987) 120 pp
  74. N. Ghoussoub, B. Maurey, W. Schachermayer: A counterexample to a problem about points of continuity in Banach spaces, Proc. A.M.S., Vol. 99, No. 2 (1987)
  75. N. Ghoussoub, B. Maurey: Hδ-embeddings in Hilbert space and Optimization on Gδ-sets. Memoirs of the A.M.S., No. 349 (l986) 102 pp
  76. N. Ghoussoub, B. Maurey: Gδ-embeddings in Hilbert space, Journal of Functional Analysis, Vol. 61, No. 1 (1985) p. 72-97
  77. N. Ghoussoub, B. Maurey: The Asymptotic-norming and the Radon-Nikodym properties are equivalent in separable Banach spaces, Proc. A.M.S., Vol. 94, No. 4 (1985) p. 665-671
  78. N. Ghoussoub, B. Maurey: On the Radon-Nikodym property in Function spaces. Proceedings of NSF-CBMS regional Conference at the University of Missouri, Springer-Verlag (1985) p. 65-71
  79. N. Ghoussoub: Subadditive ergodic theory in general function spaces. Séminaire d'Analyse- Publications de l'Université de Paris VII (1985) p. 157-177
  80. N. Ghoussoub, M. Talagrand: A non-completely continuous operator on L1(G) whose random Fourier transform is in c0(Ĝ). Proc. A.M.S., Vol. 92, No. 2 (1984) p. 229-332
  81. N. Ghoussoub, W. B. Johnson: Counterexamples to several problems on the factorization of bounded linear operators, Proc. A.M.S., Vol. 92, No. 2 (1984) p. 233-238
  82. N. Ghoussoub, B. Maurey: Counterexamples to several problems on Gδ-embeddings, Proc. A.M.S., Vol. 92, No. 3 (1984) p. 409-412
  83. N. Ghoussoub, P. Saab: Weak Compactness in spaces of Bochner integrable functions and the Radon-Nikodym property. Pacific J. of Math, Vol. 110, No. 1 (1984) p. 65-70
  84. N. Ghoussoub: Positive embeddings of C(Δ), L1, l 1 (Γ) and (Σn ⊕ l∞n)l 1 , Math Annalen 262 (1983) p. 461-472
  85. N. Ghoussoub, H.P. Rosenthal: Martingales, Gδ-embeddings and Quotients of L1. Math Annalen 264 (1983) p. 321-332
  86. N. Ghoussoub, S. Szarek: A note on sign-preserving operators on L1. Séminaire d'Analyse - Publications de l'Université Paris VII (1983) p. 133-138
  87. N. Ghoussoub: Some remarks concerning Gδ-embeddings and semiquotient maps. The Longhorn seminar - A Publication of The University of Texas at Austin (1982-83)
  88. N. Ghoussoub: Martingales of increasing functions - Proceedings of the conference on martingales theory in harmonic analysis and Banach spaces - Springer-Verlag, Vol. 939, No. 10 (1982) p. 62-72
  89. N. Ghoussoub: Riesz spaces valued measures and processes. Bulletin de la Société Mathematique de France, II. 110 (1982) p. 233-257
  90. N. Ghoussoub, E. Saab: On the range of basically scattered vector measures. Indiana Journal of Mathematics 31, II (1982) p. 247-253
  91. N. Ghoussoub: Renorming dual Banach lattices, Proc. A.M.S., Vol. 84, No. 4 (1982) p. 521-524
  92. W. J. Davis, N. Ghoussoub, J. Lindenstrauss: A lattice renorming theorem and applications to vector valued processes, Trans A.M.S., Vol. 263 (1981) p. 531-540
  93. N. Ghoussoub: Convexity and differentiability in Banach spaces. State of the Art. Annals of the CEREMADE. (Mathematical techniques of optimization, control and decision) Birkhauser. Bost. Inc. (1981) p. 47-62
  94. T. Figiel, N. Ghoussoub, W. B. Johnson: On the structure of non-weakly compact operators on Banach lattices, Math Annalen 257 (1981) p. 317-344
  95. N. Ghoussoub: On operators fixing copies of c0 and l∞. Séminaire d'Analyse fonctionnelle- Publication de l'Ecole Polytechnique - Paris (1980/1981)
  96. N. Ghoussoub, E. Saab: On the weak Radon-Nikodym property. Proceedings of A.M.S. 81 (1980) p. 81-84
  97. W. J. Davis, N. Ghoussoub, J. Lindenstrauss: Renorming Separable Banach Lattices. Seminaire Choquet, 19eme Année, Publications de l'Université Paris VI (1980)
  98. N. Ghoussoub: An integral representation of random probabilities and its applications. Seminaire de probabilités XVI - Springer-Verlag (1980/1981) 32 pp
  99. N. Ghoussoub: On spaces with local unconditional structure, Séminaire d'Analyse fonctionnelle- Publication de l'Ecole Polytechnique - Paris (1979-1980)
  100. N. Ghoussoub, M. Steele: Vector-valued subadditive processes and applications in probability. Annals of Probability, Vol 8, No. 1 (1980), p. 83-95
  101. N. Ghoussoub, M. Talagrand: Convergence faible des potentiels de Doob vectoriels. C. R. Acad. Sci. t. 288, Serie A, Paris (1979) p. 165-172
  102. R.V. Chacon, N. Ghoussoub: Embeddings in Brownian motion. Ann. Inst. Henri Poincaré XV, No. 3 (1979) p. 287-292
  103. N. Ghoussoub, S.R. Foguel: Ornstein-Métivier-Brunel theorem revisited. Ann. Inst. Henri Poincaré XV, No. 3 (1979) p. 293-301
  104. N. Ghoussoub, M. Talagrand: Order dentability and Radon-Nikodym property in Banach lattices, Math Annalen 243 (1979) p. 217-225
  105. N. Ghoussoub: Summability and vector amarts. J. Mult. Analysis, Vol 9, No. 1 (1979) p. 173-178
  106. N. Ghoussoub: Orderamarts: A class of asymptotic martingales. J. Mult. Analysis, Vol 9, No. 1 (1979) p. 165-172
  107. N. Ghoussoub, Y. Benyamini: Une caracterisation probabiliste de l1. C.R. Acad. Sci. t.286 Serie A, Paris (1978) p. 795-797
  108. N. Ghoussoub, L. Sucheston: A refinement of the Riesz decomposition of amarts and semi-amarts. J. Mult. Analysis, Vol. 8, No. 1 (1978) p. 146-150
  109. N. Ghoussoub, M. Talagrand: A generalized Chacon's inequality and order convergence of processes. Seminaire Choquet, Publications de l' Université Paris VI, 1977/78
  110. N. Ghoussoub: Banach lattices valued amarts. Annales de l'Institut Henri Poincaré XII, No. 2 (1977) p. 159-169
  111. N. Ghoussoub: Processus de Harris abstraits, Annales de l'Institut Henri Poincaré XI, No. 4 (1975) p. 381-395
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