@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}, publisher = {Dunod}, address = {Paris}, volume = {34}, number = {2}, year = {2000}, mrnumber = {1765671}, zbl = {0963.76052}, language = {en}, url = {http://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 PP - Paris UR - http://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 %C Paris %U http://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, Tome 34 (2000) no. 2, pp. 477-499. http://www.numdam.org/item/M2AN_2000__34_2_477_0/
[1] Symmetric rearrangement is sometimes continuous. J. Amer. Math. Soc. 2 (1989) 683-772. | MR | Zbl
and ,[2] 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. | MR | Zbl
and ,[3] On a free boundary problem arising in plasma physics. Nonlinear Anal. 4 (1980) 415-436. | MR | Zbl
and ,[4] Duality methods for solving variational inequalities. Comp. and Math. Appl. 7 (1981) 43-58. | MR | Zbl
and ,[5] Numerical Solution of a Nonlocal Problem Arising in Plasma Physics. Mathematical and Computing Modelling. 27 (1998) 45-59. | MR
and ,[6] Numerical Simulation and Optimal Control in Plasma Physics, Wiley, Gauthier-Villars (1989). | MR | Zbl
,[7] Existence and Control of plasma equilibrium in a tokamak. SIAM J. Math. Anal. 17 (1986) 1158-1177. | MR | Zbl
, and ,[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). | MR | Zbl
,[11] Equimesurable rearrangements of functions, Queen's University (1971). | MR | Zbl
and ,[12] Introduction to Numerical Linear Algebra and Optimization, Cambrigde University Press (1989). | MR | Zbl
,[13] The Continuity of the Rearrangement in W1,p (R). Annali della Scuola Normale Superiore di Pisa. Série IV 11 (1984) 57-85. | EuDML | Numdam | MR | Zbl
,[14] Methods of Mathematical Physics, vol I., Interscience Pub. (1953). | MR | Zbl
and ,[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] 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. | MR | Zbl
and ,[19] 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. | MR | Zbl
and ,[20] Convex Analysis and Variational Problems, North-Holland (1976). | MR | Zbl
and ,[21] Critical Point Approximation Through Exact Regularization. Math. Comp. 50 (1988) 139-153. | MR | Zbl
and ,[22] Ideal Magnetohydrodynamics. Plenum Press (1987).
,[23] Variational principles and free-boundary problems, John Wiley and Sons (1982). | MR | Zbl
,[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] Determination of Hydromagnetic Equilibria. Phys. Fluids 27 (1984) 2101-2120. | MR | Zbl
and ,[27] Inequalities, Cambridge University Press (1964). | JFM | MR | Zbl
, and ,[28] Equilibrium calculation for helical axis Stellarators. Phys. Fluids 27 (1984) 2101-2120. | Zbl
and ,[29] Non convex methods for computing free boundary equilibria of axially symmetric plasmas, Rapport de Recherche, I.N.R.I.A. (1981). | MR | Zbl
and ,[30] Equilibrium of Magnetically Confined Plasma in a Toriod. Physics of Fluids 1, No. 4, (1958) 265-274. | MR | Zbl
and ,[31] Optimum desing with lagrangian finite elements: desing of an electromagnet, Rapport de Recherche, I.N.R.I.A (1977).
and ,[32] On a class of nonlinear problems with positive, increasmg, convex nonlinearity. Comm. Par. Diff. Eq. 5 (1980) 791-836. | Zbl
and ,[33] Isoperimetric inequalities in parabolic equations. Annali della Scuola Normale Superiore di Pisa. Séne IV 13, No. 1, (1986) 51-73. | EuDML | Numdam | MR | Zbl
and ,[34] Directional Derivative of the Increasing Rearrangement Mapping and Application to a Queer Differential Equation in Plasma Physics. Duke Mathematical Journal 48 (1981) 475-495. | MR | Zbl
and ,[35] 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. | MR | Zbl
and ,[36] Inégalités isopérmétriques et applications en physique, Hermann (1984). | MR | Zbl
,[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] Introduction to the monotone and relative rearrangements and applications, Rapport, Département de Mathématiques, Université de Poitiers (1993).
, and ,[40] Isopermetric inequalities in mathematical physics, Princenton Univ. Press (1951). | MR
and ,[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. | MR | Zbl
,[43] A differentiability result for the relative rearrangement. Diff. Int. Eq. 2 (1989) 363-377. | MR | Zbl
,[44] Relative rearrangement for highly nonlinear equations. Nonlinear Analysis. Theory, Meth. and Appl. 24 (1995) 493-507. | MR | Zbl
,[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. | MR | Zbl
,[47] 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. | MR | Zbl
and ,[48] 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. | EuDML | MR | Zbl
and ,[49] A co-area formula with applications to monotone rearrangement and to regularity. Arch. Rational Mech. Anal. 109 (1991) 213-238. | MR | Zbl
and ,[50] Convex Analysis, Princeton Unviversity Press (1970). | MR | Zbl
,[51] On agneto-hydrodynamical equilibrium configurations. Soviet Physics JETP, 6 (1958) 5456-554. | MR | Zbl
,[52] Rearrangements of functions and and Partial Differential Equations. Nonlinear Diffusion Problems, A. Fasano and M. Primicerio Eds, Springer-Verlag (1986) 153-178. | MR | Zbl
,[53] Rearrangements and PDE. Inequalities, fifty years on from Hardy, Littlewood and Pòlya, W.N. Everitt Ed., Marcel Dekker Inc. (1991) 211-230. | MR | Zbl
,[54] Assembling a rearrangement. Arch. Rat. Mech. Anal. 98 (1987) 85-93. | MR | Zbl
,[55] A nonlinear eigenvalue problem equilibrium shape of a confined plasma. Arch. Rat. Mech. Anal. 65 (1975) 51-73. | MR | Zbl
,[56] Remarks on a free boundary problem arising in plasma physics. Comm. Par. Diff. Eq. 2 (1977) 563-585. | MR | Zbl
,[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. | MR | Zbl
,[60] A Duality Principle for Non-convex Optimisation and the Calculus the Variations. Arch. Rat. Mech. Anal. 71 (1979) 41-61. | MR | Zbl
,[61] Matrix Iterative Analysis, Prentice-Hall Inc. (1962). | MR | Zbl
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