Convex symmetrization and applications

Angelo Alvino; Vincenzo Ferone; Guido Trombetti; Pierre-Louis Lions

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 2, page 275-293
  • ISSN: 0294-1449

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Alvino, Angelo, et al. "Convex symmetrization and applications." Annales de l'I.H.P. Analyse non linéaire 14.2 (1997): 275-293. <http://eudml.org/doc/78411>.

@article{Alvino1997,
author = {Alvino, Angelo, Ferone, Vincenzo, Trombetti, Guido, Lions, Pierre-Louis},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {symmetrization; isoperimetric inequality; rearrangement},
language = {eng},
number = {2},
pages = {275-293},
publisher = {Gauthier-Villars},
title = {Convex symmetrization and applications},
url = {http://eudml.org/doc/78411},
volume = {14},
year = {1997},
}

TY - JOUR
AU - Alvino, Angelo
AU - Ferone, Vincenzo
AU - Trombetti, Guido
AU - Lions, Pierre-Louis
TI - Convex symmetrization and applications
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 2
SP - 275
EP - 293
LA - eng
KW - symmetrization; isoperimetric inequality; rearrangement
UR - http://eudml.org/doc/78411
ER -

References

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  2. [ALT] A. Alvino, P.-L. Lions and G. Trombetti, Comparison results for elliptic and parabolic equations via Schwarz symmetrization, Ann. Inst. Henri Poinearé, Analyse Nonlineaire, Vol. 7, 1990, pp. 37-65. Zbl0703.35007MR1051227
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  4. [Ba] C. Bandle, On symmetrizations in parabolic equations, J. Anal. Math., Vol. 30, 1976, pp. 98-112. Zbl0331.35036MR442477
  5. [BFM] M.F. Betta, V. Ferone and A. Mercaldo, Regularity for solutions of nonlinear elliptic equations, Bull. Sci. Math., Vol. 118, 1994, pp. 539-567. Zbl0842.35014MR1309088
  6. [BZ] Yu.D. Burago and V.A. Zalgaller, Geometric Inequalities, Springer-Verlag, Berlin, 1988. Zbl0633.53002MR936419
  7. [Bu] H. Buseman, The isoperimetric problem for Minkowski area, Amer. J. Math., Vol. 71, 1949, pp. 743-762. Zbl0038.10301MR31762
  8. [DG] E. De Giorgi, Su una teoria generale della misura (r — 1)-dimensionale in uno spazio ad r dimensioni, Ann. Mat. Pura e Appl., Vol. 36, 1954, pp. 191-213. Zbl0055.28504MR62214
  9. [FP] V. Ferone and M.R. Posteraro, Symmetrization results for elliptic equations with lower-order terms, Atti Sem. Mat. Fis. Univ. Modena, Vol. 39, 1991, pp. 47-61. Zbl0796.35034MR1179021
  10. [FPV] V. Ferone, M.R. Posteraro and R. Volpicelli, An inequality concerning rearrangements of functions and Hamilton-Jacobi equations, Arch. Rat. Mech. Anal., Vol. 125, 1993, pp. 257-269. Zbl0787.35020MR1245072
  11. [GN] E. Giarrusso and D. Nunziante, Symmetrization in a class of first-order Hamilton-Jacobi equations, Nonlinear Analysis T.M.A., Vol. 8, 1984, pp. 289-299. Zbl0543.35014MR739660
  12. [G] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Basel, 1984. Zbl0545.49018MR775682
  13. [La] S.R. Lay, Convex sets and their applications, J. Wiley and Sons, New York, 1982. Zbl0492.52001MR655598
  14. [Li] P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations, Pitman, London, 1982. Zbl0497.35001MR667669
  15. [M] V.G. Maz'ja, Sobolev spaces, Springer-Verlag, Berlin, 1985. MR817985
  16. [MR] J. Mossino and J.M. Rakotoson, Isoperimetric inequalities in parabolic equations, Ann. Scuola Norm. Sup. Pisa, Vol. 13, 1986, pp. 51-73. Zbl0652.35053MR863635
  17. [PS] G. Pólya and G. Szegö, Isoperimetric inequalities in mathematical physics, Ann. Math. Studies, No. 27, Princeton University Press, Princeton, 1951. Zbl0044.38301MR43486
  18. [R] R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970. Zbl0193.18401MR274683
  19. [T1] G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura e Appl., Vol. 110, 1976, pp. 353-372. Zbl0353.46018MR463908
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Citations in EuDML Documents

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  1. Jean Van Schaftingen, Anisotropic symmetrization
  2. Jaroslav Jaroš, Picone’s identity for a Finsler p -Laplacian and comparison of nonlinear elliptic equations
  3. Lorenzo Brasco, On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique
  4. Marino Belloni, Bernd Kawohl, The pseudo- p -Laplace eigenvalue problem and viscosity solutions as p
  5. Adele Ferone, Roberta Volpicelli, Minimal rearrangements of Sobolev functions : a new proof
  6. Nicola Fusco, Simmetrizzazione e disuguaglianze di tipo Pòlya-Szegö
  7. Marino Belloni, Bernd Kawohl, The pseudo--Laplace eigenvalue problem and viscosity solutions as → ∞
  8. Dario Cordero-Erausquin, Quelques exemples d'application du transport de mesure en géométrie euclidienne et riemannienne
  9. Guido Trombetti, Metodi di simmetrizzazione nelle equazioni alle derivate parziali

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