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Applicable Analysis
An International Journal
Volume 80, 2001 - Issue 1-2
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Original Articles

General pointwise relations for the relative rearrangement and applications

J.M. Rakotoson Département de Mathématiques, Université de Poitiers, Futuroscope Cedex, SP2MI 86960, France
Pages 201-232 | Received 06 Jul 2001, Published online: 02 May 2007

  • Alvino A. Ferone V. Trombetti G. Estimates for the gradient of solutions of nonlinear elliptic equations with L1 data Preprint Universita degli Studi di Napoli “Federico II” 1998 Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Complesso Universitario Monte S. Angelo Via Cintia 80126 Napoli 60 (to appear in Ann. di Pura ed Applicata)
  • Alvino , A. 1977 . Sulla diseguaglianza di Sobolev in spazi di Lorentz . Bolletino U.M.I. , 14-A ( 5 ) : 148 – 156 .
  • Alvino , A. , Lions , P.L. and Trombetti , G. 1989 . On optimization problems with prescribed rearrangements . Nonlinear Analysis T.M.A. , 13 ( 5 ) : 185 – 220 .
  • Alvino , A. and Trombetti , G. 1978 . Sulle migliori costanti di maggiorazione per una classe di equazioni ellittiche degeneri . Ricerche Mat. , 27 ( 5 ) : 413 – 428 .
  • Betta , F. and Mercaldo , A. 1978 . Existence and regularity results for a nonlinear elliptic equations . Rendiconti di Matematica 11 , VII ( 5 ) : 737 – 759 .
  • Burton , G.R. and Ryan , E.P. 1988 . On reachable sets and extremal rearrangements of control functions . SIAM J. Control Optim. , 6 ( 5 ) : 1481 – 1489 .
  • Bennett , C. and Sharpley , R. 1983 . Interpolation of operators , Academic Press .
  • Brother , J.E. and Ziemer , W.P. 1988 . Minimal rearrangements of Sobolev functions . J. Reine Angew. Math., Queen's Papers in Pure and Applied Mathematics , 384 : 153 – 179 .
  • Cianchi , A. and Pick Sobolev , L. 1998 . Imbedding into BMO, VMO . L∞ Ark. Mat. , 36 : 317 – 340 .
  • Chong , K.M. and Rice , N.M. 1971 . Equimesurable Rearrangements of Functions , 28 Queen's University, Ontario
  • Douglas , R.J. 1994 . Rearrangements of functions on unbounded domains , Vol. 124A , 621 – 644 . Proceedings of the Royal Society of Edingburg .
  • Dolzmann , G. , Hungerbühler , N. and Müller , S. 2000 . Uniqueness and maximal regukarity for nonlinear elliptic systems of n-Laplace type with measure valued right hard side . J. Reine Angew. Math. , 1 : 1 – 35 .
  • Diaz , J.I. , Nagai , T. and Rakotoson , J.M. 1998 . Symmetrization Techniques on Unbounded Domains: Application to a Chemotaxis System on . J. of Diff. Equations , 145 ( 1 ) : 156 – 183 .
  • Diaz , J.J. , Padial , J.F. and Rakotoson , J.M. 1998 . Mathematical treatment of the magnetic confinement in a current carrying Stellerator . Nonlinear Analysis TMA. , 145 ( 1 ) : 857 – 887 .
  • Diaz , J.I. and Rakotoson , J.M. 1996 . On a nonlocal stationary free boundary problem arising in the confinement of a plasma in a Stellerator geometry . Arch. Rat. Mech. Anal. , 134 ( 1 ) : 53 – 95 .
  • Friedmam , A. and McLeod , B. 1986 . Strict inequalities for integrals of decreasingly rearranged functions , Vol. 102A , 277 – 289 . Proceeding of the Royal of Edinburgh .
  • Ferone , A. and Posteraro , M.R. 1991 . A remark on a comparison theorem . Comm. In PDE , 16 : 1255 – 1262 .
  • Ferone , A. and Volpicelli , R. 1997 . Some relations between Pseudo-rearrangement and Relative rearrangement . Université de Poitiers D´ de Mathématiques , 113 (2000) in Nonlinear Analysis, 41, 855-869.
  • Kawohl , B. 1985 . “ Rearrangements and convexity of level sets in P.D.E. ” . In Lecture Notes in Math. , Vol. 1150 , Berlin : Springer . New York
  • Korkut , L. , Pasic , M. and Zubrinic , D. 2000 . A singular ODE related to quasilinear elliptic equations . EJDE , 2000 ( 12 ) : 1 – 37 .
  • Mazja , V. 1985 . Sobolev spaces , Tokyo : Springer-Verlag . Heidelberg, New York
  • Migliaccio , L. 1983 . Sur une condition de Hardy , Vol. 297 , 25 – 28 . Paris : C.R. hebd. Séanc. Acad. Sci. . Littlewood, Polyà
  • Mossino , J. 1984 . Inégalités isopérimétriques et applications en physique , Herman .
  • Mossino , J. and Rakotoson , J.M. 1986 . Isoperimetric inequalities in prabolic equations . Annali della Scuola Normale Superiore di Pisa , IV XIII 1.
  • Mossino , J. and Temam , R. 1981 . Directional derivate of the increasing rearrangement mapping and application to a queer differential equation in plasma physics . Duke Math. J. , 48 : 475 – 495 .
  • Rakotoson , J.M. 1988 . Some properties of the relative rearrangement . J. Math. Anal. Appl. , 135 ( 2 ) : 488 – 500 .
  • Rakotoson , J.M. 1999 . Galerkin approximation, strong continuity of the relative rearrangement map and application to plasma physics equations . Differential and Integral Equations , 12 ( 1 ) : 67 – 81 .
  • Rakotoson , J.M. 1989 . A differentiability result for the relative rearrangement . Differential and Integral Equations , 2 ( 3 ) : 363 – 377 .
  • Simon , J. and Rakotoson , J.M. 1993 . Relative rearrangement on a measure space: application to the regularity of weighted monotone rearrangement . Appl. Math. Lett. , I ( II ) : 75 – 82 .
  • Simon , J. and Rakotoson , J.M. 1997 . Relative rearrangement on a finite measure space: application to the regularity of weighted monotone rearrangement . Revista de la Real Academia de Ciences de Madrid , 91 ( 1 ) : 17 – 31 .
  • Rakotoson , J.M. and Temam , R. 1987 . Relative rearrangement in quasilinear elliptic variational inequalities . Indiana university Math. J. , 36 ( 4 ) : 757 – 810 .
  • Rakotoson , J.M. and Temam , R. 1990 . A co-area formula with applications to monotone rearrangement and to regularity . Arch. Ratio. Mech. and Analysys , 109 ( 3 ) : 213 – 238 .
  • Ryff , J.V. 1968 . Majorized functions and measures . Indag.Math , 30 ( 3 ) : 431 – 437 .
  • Sperner , E. 1973 . Zur Symmetrisierung von Funktionen auf Sphären . Math. Z. , 134 ( 3 ) : 317 – 327 .
  • Simon B. Rérrangement relatif sur un espace mesuré et applications 1994 Université Poitiers
  • Talenti , G. 1976 . Elliptic equations and rearrangements . Ann. Scuola Norm. Sup. Pisa , 4 ( 3 ) : 697 – 718 .
  • Temam , R. 1979 . “ Monotone rearrangement of a functions and the Grad-Mercier equation of plasma physics ” . In Recent Methods in Nonlinear Analysis and Applications , Edited by: de Giorgi , E. , Magenes , E. and Mosco , U. Bologna : Petragora Editrice .

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