Complutense University Library

Elliptic-equations and steiner symmetrization


Díaz Díaz, Jesús Ildefonso and Alvino , A. and Lions, P.L. and Trombetti, G. (1992) Elliptic-equations and steiner symmetrization. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique , 314 (13). pp. 1015-1020. ISSN 0764-4442

[img] PDF
Restringido a Repository staff only hasta 31 December 2020.


Official URL:;2-G/pdf


We present a new proof of comparison results via Steiner symmetrization for solutions of elliptic equations. This proof relies upon a "level sets" argument.

Item Type:Article
Uncontrolled Keywords:Steiner symmetrization
Subjects:Sciences > Mathematics > Differential equations
ID Code:16258

Alvino, A., Diaz, J. I., Lions, P. L., and Trombetti, G., Equation elliptiques et symétrization de Steiner, C. R. Acad. Sci. Paris Sér. I Math. 314, 1992, pp. 1015–1020.

Alvino, A., Lions, P. L., and Trombetti, G., A remark on comparison results via symmetrization, Proc. Edinburgh Math. Soc. 102A, 1986, pp. 37–48.

Alvino, A., Lions, P. L., and Trombetti, G., Comparison results for elliptic and parabolic equations via Schwarz symmetrization, Ann. Inst. H. Poincaré Anal. Non Linéaire 7, 1990, pp. 37–65.

Alvino, A., Lions, P. L., and Trombetti, G., Comparison results for elliptic and parabolic equations via symmetrization: a new approach, Differential Integral Equations 4, 1991, pp. 25–50.

Alvino, A., and Trombetti, G., Sulle migliori costanti di maggiorazioni per una classe di equazioni ellittiche degeneri, Ricerche Mat. 27, 1978, pp. 413–428.

Alvino, A., and Trombetti, G., Equazioni ellittiche con termini di ordine inferiore e riordinamenti, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (8) 66, 1979, pp. 194–200.

Bandle, C., Isoperimetric Inequalities and Applications, Pitman, London, 1980.

Bandle, C., On symmetrization in parabolic equations, J. Anal. Math. 30, 1976, pp. 98–112.

Bandle, C., and Kawhol, B., Application de la symétrization de Steiner aux problèmes de Poisson, preprint, 1992.

Chiti, G., Norme di Orlicz delle soluzioni di una classe di equazioni ellittiche, Boll. Un. Mat. Ital. A (5) 16, 1979, pp. 178–185.

De Giorgi, E., Su una teoria generale della misura (r - 1)-dimensionale in uno spazio ad r-dimensioni, Ann. Mat. Pura Appl. 36, 1954, pp. 191–213.

Hardy, G. H., Littlewood, J. E., and Polya, G., Inequalities, Cambridge University Press, 1964.

Laurence, P., and Stredulinsky, E. W., A bootstrap argument for Grad generalized differential equations, Indiana Univ. Math. J. 38, 1989, pp. 377–415.

Lions, P. L., Quelques rémarques sur la symétrization de Schwarz, In: Nonlinear Partial Differential Equations and Their Applications, Coll. de France Semin., 1, Pitman, London, 1980.

Maderna, C., Pagani, D., and Salsa, S., Quasilinear elliptic equations with quadratic growth in the gradient, J. Differential Equations 97, 1992, pp. 54–70.

Mossino, J., and Rakotoson, J. M., Isoperimetric inequalities in parabolic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 13, 1986, pp. 51–73.

Rakotoson, J.-M., and Simon, B., Relative rearrangement on a measure space; application to the regularity of weighted monotone rearrangements. Parts I and II, Appl. Math. Lett. 6, 1993, pp. 75–82.

Talenti, G., Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 3, 1976, pp. 697–718.

Talenti, G., Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces, Ann. Mat. Pura Appl. 120, 1979, pp. 159–184.

Talenti, G., Linear elliptic P.D.E.'S: level sets, rearrangements and a priori estimates of solutions, Boll. Un. Mat. Ital. B (6), 4, 1985, pp. 917–949.

Weinberger, H., Symmetrization in uniformly elliptic problems. Studies in Math. Anal., Stanford University Press, 1962.

Deposited On:10 Sep 2012 09:35
Last Modified:07 Feb 2014 09:26

Repository Staff Only: item control page