Free Access
Volume 34, Number 2, March/April 2000
Special issue for R. Teman's 60th birthday
Page(s) 477 - 499
Published online 15 April 2002
  1. F. Almgren and E. Lieb, Symmetric rearrangement is sometimes continuous. J. Amer. Math. Soc. 2 (1989) 683-772. [MathSciNet] [Google Scholar]
  2. E. Beretta and M. Vogelius, Symmetric rearrangement is sometimes continuous, An inverse problem originating from Magnetohydrodynamics II: the case of the Grad-Shafranov equation. Indiana University Mathematics Journal 41 (1992) 1081-1117. [CrossRef] [MathSciNet] [Google Scholar]
  3. H. Berestycki and H. Brezis, On a free boundary problem arising in plasma physics. Nonlinear Anal. 4 (1980) 415-436. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. Bermúdez and C. Moreno, Duality methods for solving variational inequalities. Comp. and Math. Appl. 7 (1981) 43-58. [Google Scholar]
  5. A. Bermúdez and M.L. Seoane, Numerical Solution of a Nonlocal Problem Arising in Plasma Physics. Mathematical and Computing Modelling. 27 (1998) 45-59. [Google Scholar]
  6. J. Blum, Numerical Simulation and Optimal Control in Plasma Physics, Wiley, Gauthier-Villars (1989). [Google Scholar]
  7. J. Blum, T. Gallouët and J. Simon, Existence and Control of plasma equilibrium in a tokamak. SIAM J. Math. Anal. 17 (1986) 1158-1177. [CrossRef] [MathSciNet] [Google Scholar]
  8. A.H. Boozer, Establishment of magnetic coordinates for given magnetic field. Phys. Fluids 25 (1982) 520-521. [CrossRef] [Google Scholar]
  9. H. Brezis, Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North-Holland (1973). [Google Scholar]
  10. G. Chiti, Rearrangements of functions and convergence in Orlicz spaces. Applicable Analysis 9 (1979). [Google Scholar]
  11. K.M. Chong and N.M. Rice, Equimesurable rearrangements of functions, Queen's University (1971). [Google Scholar]
  12. P.G. Ciarlet, Introduction to Numerical Linear Algebra and Optimization, Cambrigde University Press (1989). [Google Scholar]
  13. J.M. Coron, The Continuity of the Rearrangement in Formula . Annali della Scuola Normale Superiore di Pisa. Série IV 11 (1984) 57-85. [Google Scholar]
  14. R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. I., Interscience Pub. (1953). [Google Scholar]
  15. J.I. Díaz, Modelos bidimensionales de equilibrio magnetohidrodinámico para Stellarators. Formulación global de las ecuacion es diferenciales no lineales y de las condiciones de contorno, CIEMAT, Informe #1 (1991). [Google Scholar]
  16. J.I. Díaz, Modelos bidimensionales de equilibrio magnetohidrodinámico para Stellarators. Resultados de existencia de soluciones, CIEMAT, Informe #2 (1992). [Google Scholar]
  17. J.I. Díaz, Modelos bidimensionales de equilibrio magnetohidrodinámico para Stellarators. Multiplicidad y dependencia de parámetros, CIEMAT, Informe #3 (1993). [Google Scholar]
  18. J.I. Díaz and J.M.Rakotoson, On a two-dimensional stationary free boundary problem arising in the confinement of a plasma in a Stellarator. C.R. Acad. Sci. Paris Serie I 317 (1993) 353-358. [Google Scholar]
  19. J.I. Díaz and J.M. Rakotoson, On a nonlocal stationary free boundary problem arising in the confinement of a plasma in a Stellarator geometry. Arch. Rat. Mech. Anal. 134 (1996) 53-95. [CrossRef] [Google Scholar]
  20. I.Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland (1976). [Google Scholar]
  21. E. Fernández-Cara and C. Moreno, Critical Point Approximation Through Exact Regularization. Math. Comp. 50 (1988) 139-153. [CrossRef] [MathSciNet] [Google Scholar]
  22. J.P. Freidberg, Ideal Magnetohydrodynamics, Plenum Press (1987). [Google Scholar]
  23. A. Friedman, Variational principles and free-boundary problems, John Wiley and Sons (1982). [Google Scholar]
  24. R. Glowinski, Numerical methods for non linear variational problems, Springer Verlag (1984). [Google Scholar]
  25. H. Grad, Mathematical problem arising in plasmas physics. Proc. Intern. Congr. Math. Nice (1970). [Google Scholar]
  26. J.M. Greene and J.L. Johnson, Determination of Hydromagnetic Equilibria. Phys. Fluids 27 (1984) 2101-2120 [Google Scholar]
  27. G.H. Hardy, J.E. Littlewood and G. Polya, Inequalities, Cambridge University Press (1964). [Google Scholar]
  28. T.C. Hender and B.A. Carreras, Equilibrium calculation for helical axis Stellarators. Phys. Fluids 27 (1984) 2101-2120. [CrossRef] [Google Scholar]
  29. B.Heron and M.Sermange, Non convex methods for computing free boundary equilibria of axially symmetric plasmas, Rapport de Recherche, I.N.R.I.A. (1981). [Google Scholar]
  30. M.D. Kruskal and R.M. Kulsrud, Equilibrium of Magnetically Confined Plasma in a Toriod. Physics of Fluids 1, No. 4, (1958) 265-274. [Google Scholar]
  31. A. Marrocco and O. Pironneau, Optimum desing with lagrangian finite elements: desing of an electromagnet, Rapport de Recherche, I.N.R.I.A. (1977). [Google Scholar]
  32. F. Mignot and J.P. Puel, On a class of nonlinear problems with positive, increasing, convex nonlinearity. Comm. Par. Diff. Eq. 5 (1980) 791-836. [CrossRef] [Google Scholar]
  33. J. Mossin and J.M. Rakotoso, Isoperimetric inequalities in parabolic equations. Annali della Scuola Normale Superiore di Pisa. Série IV 13, No. 1, (1986) 51-73. [Google Scholar]
  34. J. Mossino and R. Temam, Directional Derivative of the Increasing Rearrangement Mapping and Application to a Queer Differential Equation in Plasma Physics. Duke Mathematical Journal 48 (1981) 475-495. [CrossRef] [MathSciNet] [Google Scholar]
  35. J. Mossino and R. Temam, Free boundary problems in plasma physics, review of results and new developments. Free Boundary Problems: theory and applications. Vol I-II. Proc. Montec atini Symposium (1981). A. Fasano and M. Primicerio Eds, Pitman (1983) 672-681. [Google Scholar]
  36. J. Mossino, Inégalités isopérmétriques et applications en physique, Hermann (1984). [Google Scholar]
  37. K. Miyamoto, Plasma Physics for Nuclear Fusion, The M.I.T. Press (1987). [Google Scholar]
  38. J.F. Padial, EDPs no lineales originadas en plasmas de fusión y filtración en medios porosos, Thesis Doctoral, Universidad Complutense de Madrid (1995). [Google Scholar]
  39. J.F. Padial, J.M.Rakotoson and L. Tello, Introduction to the monotone and relative rearrangements and applications, Rapport, Département de Mathématiques, Université de Poitiers (1993). [Google Scholar]
  40. G. Pòlya and W.N. Szegö, Isopermetric inequalities in mathematical physics, Princenton Univ. Press (1951). [Google Scholar]
  41. J.P. Puel, A nonlinear eigenvalue problem with free boundary. C.R. Acad. Sci. Paris A 284 (1977) 861-863. [Google Scholar]
  42. J.M. Rakotoson, Some properties of the relative rearrangement. J. Math. Anal. Appl. 135 (1988) 488-500. [CrossRef] [MathSciNet] [Google Scholar]
  43. J.M. Rakotoson, A differentiability result for the relative rearrangement. Diff. Int. Eq. 2 (1989) 363-377. [Google Scholar]
  44. J.M. Rakotoson, Relative rearrangement for highly nonlinear equations. Nonlinear Analysis. Theory, Meth. and Appl. 24 (1995) 493-507. [Google Scholar]
  45. J.M. Rakotoson and M.L. Seoane (in preparation). [Google Scholar]
  46. J.M. Rakotoson, Galerkin approximations, strong continuity of the relative rearrangement map and application to plasma physics equations. Diff. Int. Eq. 12 (1999) 67-81. [Google Scholar]
  47. J.M. Rakotoson and B. Simon, Relative rearrangement on a measure space. Application to the regularity of weighted monotone rearrangement. Part I-II. Appl. Math. Lett. 6 (1993) 75-78; 79-92. [Google Scholar]
  48. J.M. Rakotoson and B. Simon, Relative rearrangement on a finite measure space. Application to weighted spaces and to P.D.E. Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 91 (1997) 33-45. [Google Scholar]
  49. J.M. Rakotoson and R. Temam, A co-area formula with applications to monotone rearrangement and to regularity. Arch. Rational Mech. Anal. 109 (1991) 213-238. [CrossRef] [Google Scholar]
  50. R.T. Rockafellar, Convex Analysis, Princeton University Press (1970). [Google Scholar]
  51. V.D. Shafranov, On agneto-hydrodynamical equilibriium configurations. Soviet Physics JETP, 6 (1958) 5456-554. [Google Scholar]
  52. G.G. Talenti, Rearrangements of functions and and Partial Differential Equations. Nonlinear Diffusion Problems, A. Fasano and M. Primicerio Eds, Springer-Verlag (1986) 153-178. [Google Scholar]
  53. G.G. Talenti, Rearrangements and PDE. Inequalities, fifty years on from Hardy, Littlewood and Pòlya, W.N. Everitt Ed., Marcel Dekker Inc (1991) 211-230. [Google Scholar]
  54. G.G. Talenti, Assembling a rearrangement. Arch. Rat. Mech. Anal. 98 (1987) 85-93 [Google Scholar]
  55. R. Temam, A nonlinear eigenvalue problem: equilibrium shape of a confined plasma. Arch. Rat. Mech. Anal. 65 (1975) 51-73. [CrossRef] [Google Scholar]
  56. R. Temam, Remarks on a free boundary problem arising in plasma physics. Comm. Par. Diff. Eq. 2 (1977) 563-585. [Google Scholar]
  57. R.Temam, Monotone rearrangement of functions and the Grad-Mercier equation of plasma physics, Proc. Int. Conf. Recent Methods in Nonlinear Analysis and Applications, E. de Giogi and U. Mosco Eds (1978). [Google Scholar]
  58. R.Temam, Analyse Numerique, Presses Universitaires de France (1971). [Google Scholar]
  59. J.F. Toland, Duality in nonconvex optimization. J. Math. Appl. 66 (1978) 399-415. [Google Scholar]
  60. J.F. Toland, A Duality Principle for Non-convex Optimisation and the Calculus the Variations. Arch. Rat. Mech. Anal. 71 (1979) 41-61. [CrossRef] [Google Scholar]
  61. R.S. Varga, Matrix Iterative Analysis, Prentice-Hall Inc. (1962) [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you