Comparison results for elliptic and parabolic equations via Schwarz symmetrization

A. Alvino; G. Trombetti; P.-L. Lions

Annales de l'I.H.P. Analyse non linéaire (1990)

  • Volume: 7, Issue: 2, page 37-65
  • ISSN: 0294-1449

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Alvino, A., Trombetti, G., and Lions, P.-L.. "Comparison results for elliptic and parabolic equations via Schwarz symmetrization." Annales de l'I.H.P. Analyse non linéaire 7.2 (1990): 37-65. <http://eudml.org/doc/78215>.

@article{Alvino1990,
author = {Alvino, A., Trombetti, G., Lions, P.-L.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Schwarz symmetrization; symmetrized Dirichlet problem; comparison result; coarea formula; isoperimetric inequality; integration on level sets; Hardy's inequality; Gronwall's lemma},
language = {eng},
number = {2},
pages = {37-65},
publisher = {Gauthier-Villars},
title = {Comparison results for elliptic and parabolic equations via Schwarz symmetrization},
url = {http://eudml.org/doc/78215},
volume = {7},
year = {1990},
}

TY - JOUR
AU - Alvino, A.
AU - Trombetti, G.
AU - Lions, P.-L.
TI - Comparison results for elliptic and parabolic equations via Schwarz symmetrization
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 2
SP - 37
EP - 65
LA - eng
KW - Schwarz symmetrization; symmetrized Dirichlet problem; comparison result; coarea formula; isoperimetric inequality; integration on level sets; Hardy's inequality; Gronwall's lemma
UR - http://eudml.org/doc/78215
ER -

References

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  1. [1] A. Alvino, P.-L. Lions and G. Trombetti, C.R. Acad. Sci. Paris, T. 303, 1986. 
  2. [2] A. Alvino, P.-L. Lions and G. Trombetti, Nonlinear Anal, T.M.A., Vol. 13, 1989. Zbl0678.49003MR979040
  3. [3] A. Alvino and G. Trombetti, Ric. di Mat., Vol. 27, 1978. Zbl0403.35027MR527431
  4. [4] A. Alvino and G. Trombetti, Ric. di Mat., Vol. 30, 1981. Zbl0489.35013MR657553
  5. [5] A. Alvino and G. Trombetti, Rend. Acc. Naz. Lincei, Vol. 66, 1979. Zbl0455.35052MR606083
  6. [6] C. Bandle, Isoperimetric Inequalities and Applications, Monographs and Studies in Math.Pitman, London, 1980. Zbl0436.35063MR572958
  7. [7] C. Bandle, J. Anal. Math., Vol. 30, 1976. Zbl0331.35036
  8. [8] L. Boccardo, F. Murat and J.P. Puel, in Nonlinear Partial Differential Eq. and their Appl., Coll. de France Semin., 4, Res. Not. in Math., 84 p, Pitman, London, 1983. Zbl0588.35041MR716511
  9. [9] L. Boccardo, F. Murat and J.P. Puel, Portugaliae Math., Vol. 41, 1982. Zbl0524.35041MR766873
  10. [10] L. Boccardo, F. Murat and J.P. Puel, Ann. Sc. Norm. Sup. Pisa, Vol. 11, 1984. Zbl0557.35051MR764943
  11. [11] G. Chiti, Boll. U.M.I., Vol. 16, 1979. Zbl0398.35028MR530146
  12. [12] K.M. Chong and N.M. Rice, Equimeasurable Rearrangements of Functions, Queen's papers in pure and applied math. n° 28, Queen's Univ., Ontario, 1971. Zbl0275.46024MR372140
  13. [13] M.G. Crandall and P.-L. Lions, Trans. Am. Math. Soc., Vol. 277, 1983. Zbl0599.35024MR690039
  14. [14] E. De Giorgi, Ann. Mat. Pura e Appl., Vol. 36, 1954. Zbl0055.28504
  15. [15] W. Fleming and R. Rishel, Arch. Math., Vol. 11, 1960. Zbl0094.26301MR114892
  16. [16] G.H. Hardy, J.E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, 1964. 
  17. [17] B. Kawhol, Rearrangements and Convexitu of Level Sets in PDE, Springer-Verlag, 1985. MR810619
  18. [18] M.A. Krasnoselskii, Positive Solutions of Operator Equations, P. Noordhoff, 1964. Zbl0121.10604MR181881
  19. [19] P.-L. Lions, Nonlinear Partial Differential Equations and their Appl., Coll. de France Semin., 1, Pitman, London, 1980. , 
  20. [20] J.-L. Lions, Quelques méthodes de resolutions des problèmes non linéaires, Gauthier-Villars, 1968. 
  21. [21] J. Mossino, Inégalités isopérimétriques et applications en physique, Hermann, Paris, 1985. Zbl0537.35002MR733257
  22. [22] J. Mossino and J.M. Rokotoson, Ann. Sc. Norm. Sup. Pisa, Vol. 13, 1986. 
  23. [23] C. Maderna and S. Salsa, Ann. Mat. Pura e Appl., Vol. 148, 1987. Zbl0657.35053MR932768
  24. [24] G. Talenti, Ann. Sc. Norm. Sup. Pisa, Vol. 3, 1976. Zbl0341.35031MR601601
  25. [25] G. Talenti, Boll. U.M.I., Vol. 4-B, 1985. Zbl0602.35025
  26. [26] G. Trombetti and J.L. Vasquez, Ann. Fac. Sc. de Toulouse, Vol. 5, 1985. 
  27. [27] J.L. Vasquez, C.R. Acad. Sci. Paris, T. 295, 1982. 
  28. [28] H. Weinberger, in Studies in Math. Anal., Stanford Univ. Press, 1962. 

Citations in EuDML Documents

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  1. Francesco Chiacchio, Risultati di esistenza, regolarità e confronto per equazioni ellittiche
  2. Bruno Volzone, Operatori parabolici con termine di ordine zero: risultati di confronto
  3. Vincenzo Vespri, L -estimates for nonlinear parabolic equations with natural growth conditions
  4. Angelo Alvino, Vincenzo Ferone, Guido Trombetti, Pierre-Louis Lions, Convex symmetrization and applications
  5. Angelo Alvino, Guido Trombetti, Pierre-Louis Lions, Silvano Matarasso, Comparison results for solutions of elliptic problems via symmetrization
  6. M. R. Posteraro, Estimates for solutions of nonlinear variational inequalities
  7. B. Brandolini, C. Nitsch, C. Trombetti, New isoperimetric estimates for solutions to Monge-Ampère equations
  8. Angelo Alvino, Silvano Matarasso, Guido Trombetti, Variational inequalities and rearrangements
  9. Guido Trombetti, Metodi di simmetrizzazione nelle equazioni alle derivate parziali

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