@article{M2AN_2000__34_2_477_0,
author = {Rakotoson, Jean-Michel and Seoane, Maria Luisa},
title = {Numerical approximations of the relative rearrangement : the piecewise linear case. {Application} to some nonlocal problems},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {477--499},
year = {2000},
publisher = {Dunod},
volume = {34},
number = {2},
mrnumber = {1765671},
zbl = {0963.76052},
language = {en},
url = {https://www.numdam.org/item/M2AN_2000__34_2_477_0/}
}
TY - JOUR AU - Rakotoson, Jean-Michel AU - Seoane, Maria Luisa TI - Numerical approximations of the relative rearrangement : the piecewise linear case. Application to some nonlocal problems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2000 SP - 477 EP - 499 VL - 34 IS - 2 PB - Dunod UR - https://www.numdam.org/item/M2AN_2000__34_2_477_0/ LA - en ID - M2AN_2000__34_2_477_0 ER -
%0 Journal Article %A Rakotoson, Jean-Michel %A Seoane, Maria Luisa %T Numerical approximations of the relative rearrangement : the piecewise linear case. Application to some nonlocal problems %J ESAIM: Modélisation mathématique et analyse numérique %D 2000 %P 477-499 %V 34 %N 2 %I Dunod %U https://www.numdam.org/item/M2AN_2000__34_2_477_0/ %G en %F M2AN_2000__34_2_477_0
Rakotoson, Jean-Michel; Seoane, Maria Luisa. Numerical approximations of the relative rearrangement : the piecewise linear case. Application to some nonlocal problems. ESAIM: Modélisation mathématique et analyse numérique, Special Issue for R. Temam's 60th birthday, Tome 34 (2000) no. 2, pp. 477-499. https://www.numdam.org/item/M2AN_2000__34_2_477_0/
[1] and , Symmetric rearrangement is sometimes continuous. J. Amer. Math. Soc. 2 (1989) 683-772. | Zbl | MR
[2] and , Symmetrie 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. | Zbl | MR
[3] and , On a free boundary problem arising in plasma physics. Nonlinear Anal. 4 (1980) 415-436. | Zbl | MR
[4] and , Duality methods for solving variational inequalities. Comp. and Math. Appl. 7 (1981) 43-58. | Zbl | MR
[5] and , Numerical Solution of a Nonlocal Problem Arising in Plasma Physics. Mathematical and Computing Modelling. 27 (1998) 45-59. | MR
[6] , Numerical Simulation and Optimal Control in Plasma Physics, Wiley, Gauthier-Villars (1989). | Zbl | MR
[7] , and , Existence and Control of plasma equilibrium in a tokamak. SIAM J. Math. Anal. 17 (1986) 1158-1177. | Zbl | MR
[8] , Establishment of magnetic coordinates for given magnetic field. Phys. Fluids 25 (1982) 520-521. | Zbl
[9] , Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North-Holland (1973). | Zbl
[10] , Rearrangements of functions and convergence in Orlicz spaces. Applicable Analysis 9 (1979). | Zbl | MR
[11] and , Equimesurable rearrangements of functions, Queen's University (1971). | Zbl | MR
[12] , Introduction to Numerical Linear Algebra and Optimization, Cambrigde University Press (1989). | Zbl | MR
[13] , The Continuity of the Rearrangement in W1,p (R). Annali della Scuola Normale Superiore di Pisa. Série IV 11 (1984) 57-85. | Numdam | Zbl | MR | EuDML
[14] and , Methods of Mathematical Physics, vol I., Interscience Pub. (1953). | Zbl | MR
[15] , 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).
[16] , Modelos bidimensionales de equilibrio magnetohidrodinámico para Stellarators. Resultados de existencia de soluciones, CIEMAT, Informe #2 (1992). | MR
[17] , Modelos bidimensionales de equilibrio magnetohidrodinámico para Stellarators. Multiplicidad y dependencia de parámetros, CIEMAT, Informe #3 (1993).
[18] and , 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. | Zbl | MR
[19] and , 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. | Zbl | MR
[20] and , Convex Analysis and Variational Problems, North-Holland (1976). | Zbl | MR
[21] and , Critical Point Approximation Through Exact Regularization. Math. Comp. 50 (1988) 139-153. | Zbl | MR
[22] , Ideal Magnetohydrodynamics. Plenum Press (1987).
[23] , Variational principles and free-boundary problems, John Wiley and Sons (1982). | Zbl | MR
[24] , Numerical methods for non linear variational problems, Springer Verlag (1984). | MR
[25] , Mathematical problem arising in plasmas physics. Proc. Intern. Congr. Math. Nice (1970).
[26] and , Determination of Hydromagnetic Equilibria. Phys. Fluids 27 (1984) 2101-2120. | Zbl | MR
[27] , and , Inequalities, Cambridge University Press (1964). | Zbl | JFM | MR
[28] and , Equilibrium calculation for helical axis Stellarators. Phys. Fluids 27 (1984) 2101-2120. | Zbl
[29] and , Non convex methods for computing free boundary equilibria of axially symmetric plasmas, Rapport de Recherche, I.N.R.I.A. (1981). | Zbl | MR
[30] and , Equilibrium of Magnetically Confined Plasma in a Toriod. Physics of Fluids 1, No. 4, (1958) 265-274. | Zbl | MR
[31] and , Optimum desing with lagrangian finite elements: desing of an electromagnet, Rapport de Recherche, I.N.R.I.A (1977).
[32] and , On a class of nonlinear problems with positive, increasmg, convex nonlinearity. Comm. Par. Diff. Eq. 5 (1980) 791-836. | Zbl
[33] and , Isoperimetric inequalities in parabolic equations. Annali della Scuola Normale Superiore di Pisa. Séne IV 13, No. 1, (1986) 51-73. | Numdam | Zbl | MR | EuDML
[34] and , Directional Derivative of the Increasing Rearrangement Mapping and Application to a Queer Differential Equation in Plasma Physics. Duke Mathematical Journal 48 (1981) 475-495. | Zbl | MR
[35] and , 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. | Zbl | MR
[36] , Inégalités isopérmétriques et applications en physique, Hermann (1984). | Zbl | MR
[37] , Plasma Physics for Nuclear Fusion, The M.I.T. Press (1987).
[38] , EDPs no lineales originadas en plasmas de fusión y filtración en medios porosos, Thesis Doctoral, Universidad Complutense de Madrid (1995).
[39] , and , Introduction to the monotone and relative rearrangements and applications, Rapport, Département de Mathématiques, Université de Poitiers (1993).
[40] and , Isopermetric inequalities in mathematical physics, Princenton Univ. Press (1951). | MR
[41] , A nonlinear eigenvalue problem with free boundary, C.R. Acad. Sci. Paris A 284 (1977) 861-863. | Zbl
[42] , Some properties of the relative rearrangement. J. Math. Anal. Appl. 135 (1988) 488-500. | Zbl | MR
[43] , A differentiability result for the relative rearrangement. Diff. Int. Eq. 2 (1989) 363-377. | Zbl | MR
[44] , Relative rearrangement for highly nonlinear equations. Nonlinear Analysis. Theory, Meth. and Appl. 24 (1995) 493-507. | Zbl | MR
[45] and , (in preparation).
[46] , Galerkin approximations, strong continuity of the relative rearrangement map and application to plasma physics equations. Diff. Int. Eq. 12 (1999) 67-81. | Zbl | MR
[47] and , 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. | Zbl | MR
[48] and , 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. | Zbl | MR | EuDML
[49] and , A co-area formula with applications to monotone rearrangement and to regularity. Arch. Rational Mech. Anal. 109 (1991) 213-238. | Zbl | MR
[50] , Convex Analysis, Princeton Unviversity Press (1970). | Zbl | MR
[51] , On agneto-hydrodynamical equilibrium configurations. Soviet Physics JETP, 6 (1958) 5456-554. | Zbl | MR
[52] , Rearrangements of functions and and Partial Differential Equations. Nonlinear Diffusion Problems, A. Fasano and M. Primicerio Eds, Springer-Verlag (1986) 153-178. | Zbl | MR
[53] , Rearrangements and PDE. Inequalities, fifty years on from Hardy, Littlewood and Pòlya, W.N. Everitt Ed., Marcel Dekker Inc. (1991) 211-230. | Zbl | MR
[54] , Assembling a rearrangement. Arch. Rat. Mech. Anal. 98 (1987) 85-93. | Zbl | MR
[55] , A nonlinear eigenvalue problem equilibrium shape of a confined plasma. Arch. Rat. Mech. Anal. 65 (1975) 51-73. | Zbl | MR
[56] , Remarks on a free boundary problem arising in plasma physics. Comm. Par. Diff. Eq. 2 (1977) 563-585. | Zbl | MR
[57] , 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). | Zbl
[58] , Analyse Numérique, Presses Universitaires de France (1971). | Zbl
[59] , Duality in nonconvex optimization. J. Math. Appl. 66 (1978) 399-415. | Zbl | MR
[60] , A Duality Principle for Non-convex Optimisation and the Calculus the Variations. Arch. Rat. Mech. Anal. 71 (1979) 41-61. | Zbl | MR
[61] , Matrix Iterative Analysis, Prentice-Hall Inc. (1962). | Zbl | MR






