Comparison results for solutions of elliptic problems via symmetrization

Angelo Alvino; Guido Trombetti; Pierre-Louis Lions; Silvano Matarasso

Annales de l'I.H.P. Analyse non linéaire (1999)

  • Volume: 16, Issue: 2, page 167-188
  • ISSN: 0294-1449

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Alvino, Angelo, et al. "Comparison results for solutions of elliptic problems via symmetrization." Annales de l'I.H.P. Analyse non linéaire 16.2 (1999): 167-188. <http://eudml.org/doc/78462>.

@article{Alvino1999,
author = {Alvino, Angelo, Trombetti, Guido, Lions, Pierre-Louis, Matarasso, Silvano},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Schwarz symmetrization; linear elliptic PDE; variational inequalities},
language = {eng},
number = {2},
pages = {167-188},
publisher = {Gauthier-Villars},
title = {Comparison results for solutions of elliptic problems via symmetrization},
url = {http://eudml.org/doc/78462},
volume = {16},
year = {1999},
}

TY - JOUR
AU - Alvino, Angelo
AU - Trombetti, Guido
AU - Lions, Pierre-Louis
AU - Matarasso, Silvano
TI - Comparison results for solutions of elliptic problems via symmetrization
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1999
PB - Gauthier-Villars
VL - 16
IS - 2
SP - 167
EP - 188
LA - eng
KW - Schwarz symmetrization; linear elliptic PDE; variational inequalities
UR - http://eudml.org/doc/78462
ER -

References

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  1. [1] A. Alvino, P.-L. Lions and G. Trombetti, On optimization problems with prescribed rearrangements, Nonlin. An. TMA, Vol. 13, 1989, pp. 185-220. Zbl0678.49003MR979040
  2. [2] A. Alvino, P.-L. Lions and G. Trombetti, Comparison results for elliptic and parabolic equations via Schwarz symmetrization, Ann. I.H.P. An. Non Lin., Vol. 7, 1990, pp. 37-65. Zbl0703.35007MR1051227
  3. [3] A. Alvino, P.-L. Lions and G. Trombetti, Comparison results for elliptic and parabolic equations via symmetrization: a new approach, Diff. and Int. Eq., Vol. 4, 1991, pp. 25-50. Zbl0735.35003MR1079609
  4. [4] A. Alvino and G. Trombetti, Equazioni ellittiche con termini di ordine inferiore e riordinamenti, Atti Acc. Naz. Lincei Rend. Fis., s.8, Vol. 66, 1979, pp. 194-200. Zbl0455.35052MR606083
  5. [5] A. Alvino, S. Matarasso and G. Trombetti, Variational inequalities and rearrangements, Rend. Mat. Acc. Lincei, s.9, Vol. 3, 1992, pp. 271-285. Zbl0803.35060MR1203167
  6. [6] C. Bandle, Isoperimetric inequalities and applications, Monographs and Studies in Math., Pitman, London, 1980. Zbl0436.35063MR572958
  7. [7] C. Bandle and J. Mossino, Rearrangements in variational inequalities, Ann. Mat. Pura e Appl., Vol. 138, 1984, pp. 1-14. Zbl0563.49005MR779535
  8. [8] G. Chiti, Norme di Orlicz delle soluzioni di una classe di equazioni ellittiche, Boll. U.M.I., Vol. 16-A, 1978, pp. 179-185 Zbl0398.35028
  9. [9] 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
  10. [10] G.H. Hardy, J.E. Littlewood and G. Polya, Inequalities, Cambridge, Univ. Press, 1964. 
  11. [11] P.-L. Lions, A remark on some elliptic second order problems, Boll. U.M.I., (5) Vol. 17-A, 1980, pp. 267-270. Zbl0428.35039MR578358
  12. [12] P.-L. Lions, Non linear partial differential equations and their appl., College de France, Semin., 1, Pitman, London, 1980, pp. 308-319. Zbl0467.35008
  13. [13] C. Maderna and S. Salsa, Some special properties of solutions to obstacle problem, Rend. Sem. Mat. Un. Padova, Vol. 71, 1984, pp. 121-129. Zbl0562.35014MR769431
  14. [14] G. Talenti, Elliptic equations and rearrangements, Ann. Sc. Norm. Sup. Pisa, Vol. 3, 1976, pp. 697-718. Zbl0341.35031MR601601
  15. [15] G. Talenti, Linear elliptic P.D.E.'s: level sets, rearrangements and a priori estimates of solutions, Boll. UMI, 4-B, 1985, pp. 917-949. Zbl0602.35025MR831299

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