We give comparison results for solutions of variational inequalities, related to general elliptic second order operators, involving solutions of symmetrized problems, using Schwarz spherical symmetrization.
Si danno risultati di confronto per soluzioni di disequazioni variazionali, relative ad operatori ellittici del secondo ordine, riconducendosi a un problema a simmetria radiale con l'ausilio della simmetrizzazione di Schwarz.
@article{RLIN_1992_9_3_4_271_0, author = {Angelo Alvino and Silvano Matarasso and Guido Trombetti}, title = {Variational inequalities and rearrangements}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni}, volume = {3}, year = {1992}, pages = {271-285}, zbl = {0803.35060}, mrnumber = {1203167}, language = {en}, url = {http://dml.mathdoc.fr/item/RLIN_1992_9_3_4_271_0} }
Alvino, Angelo; Matarasso, Silvano; Trombetti, Guido. Variational inequalities and rearrangements. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 3 (1992) pp. 271-285. http://gdmltest.u-ga.fr/item/RLIN_1992_9_3_4_271_0/
[1] A remark on comparison results via symmetrization. Proc. Roy. Soc. Edin., 102A, 1986, 37-48. | MR 837159 | Zbl 0597.35005
- - ,[2] On optimization problems with prescribed rearrangements. Nonlin. An. T.M.A., 13, 1989, 185-220. | MR 979040 | Zbl 0678.49003
- - ,[3] Comparison results for elliptic and parabolic equations via Schwarz symmetrization. Ann. I.H.P. An. Non Lin., 7, 1990, 37-65; C.R. Acad. Sci., 303, Paris 1986, 947-950. | MR 1051227 | Zbl 0703.35007
- - ,[4] Comparison results for elliptic and parabolic equations via symmetrization: a new approach. Diff. and Int. Eq., 4, 1991, 25-50; C.R. Acad. Sci., 303, Paris 1986, 975-978. | MR 1079609 | Zbl 0735.35003
- - ,[5] Equazioni ellittiche con termini di ordine inferiore e riordinamenti. Atti Acc. Lincei Rend. fis., s. 8, 66, 1979, 194-200. | MR 606083 | Zbl 0455.35052
- ,[6] Sulle migliori costanti di maggiorazione per una classe di equazioni ellittiche degeneri. Ric. di Mat., 27, 1978, 413-428. | MR 527431 | Zbl 0403.35027
- ,[7] Sulle migliori costanti di maggiorazione per una classe di equazioni ellittiche degeneri e non. Ric. di Mat., 30, 1981, 15-33. | MR 657553 | Zbl 0489.35013
- ,[8] | MR 572958 | Zbl 0519.53037
, Isoperimetric inequalities and applications. Monographs and Studies in Math., Pitman, London1980.[9] Rearrangement in variational inequalities. Ann. Mat. Pura e Appl., 138, 1984, 1-14. | MR 779535 | Zbl 0563.49005
- ,[10] Sur la régularité de la solution d'inéquations elliptiques. Bull. Soc. Math. France, 96, 1968, 153-180. | MR 239302 | Zbl 0165.45601
- ,[11] Norme di Orlicz delle soluzioni di una classe di equazioni ellittiche. Boll. U.M.I., 16-A, 1978, 179-185. | Zbl 0398.35028
,[12] Su una teoria generale della misura -dimensionale in uno spazio ad dimensioni. Ann. Mat. Pura e Appl., 36, 1954, 191-213. | MR 62214 | Zbl 0055.28504
,[13] 106, Pitman, London1984. | Zbl 0595.35100
, Non linear partial differential equations and free boundaries, I. Elliptic equations. Research Notes in Math., n.[14] Isoperimetric inequalities in the parabolic obstacle problems. Journal de Math. Pures et Appl., to appear. | MR 1172451 | Zbl 0679.49011
- ,[15] Symmetrization results for elliptic equations with lower-order terms. Atti Sem. Mat. Fis. Modena, 39, 1991. | MR 1179021 | Zbl 0796.35034
- ,[16] An integral formula for total gradient variation. Arch. Math., 11, 1960, 218-222. | MR 114892 | Zbl 0094.26301
- ,[17] Estimates for solutions of elliptic equations in a limit case. Boll. Austr. Math. Soc., 36, 1987, 425-434. | MR 923824 | Zbl 0641.35019
- ,[18] | JFM 60.0169.01 | Zbl 0010.10703
- - , Inequalities. Cambridge Univ. Press, 1964.[19] 1150, Springer-Verlag, Berlin-New York1985. | MR 810619 | Zbl 0593.35002
, Rearrangements and convexity of level sets in PDE. Lecture notes in mathematics, n.[20] | MR 181881 | Zbl 0121.10604
, Positive solutions of operator equations. P. Noordhoff Ltd., Groningen1964.[21] | Zbl 0189.40603
, Quelques méthodes de resolutions des problems non linéaires. Gauthier Villar, 1968.[22] Quelques remarques sur la symétrisation de Schwarz. In: Non linear partial differential equations and their appl. College de France, Seminar, n. 1, Pitman, London1980, 308-319. | MR 631400 | Zbl 0467.35008
,[23] Some special properties of solutions to obstacle problems. Rend. Sem. Mat. Un. Padova, 71 , 1984, 121-129. | MR 769431 | Zbl 0562.35014
- ,[24] | MR 733257 | Zbl 0537.35002
, Inégalités isopérimetriques et applications en physique. Hermann, Paris1984.[25] Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa, 3, 1976, 697-718. | MR 601601 | Zbl 0341.35031
,[26] Linear elliptic P.D.E.'s: level sets, rearrangements and a priori estimates of solutions. Boll. UMI, 4-B, 1985, 917-949. | MR 831299 | Zbl 0602.35025
,[27] A symmetrization result for elliptic equations with lower-order terms. Ann. Fac. Sci. de Toulose, 7, 1985, 137-150. | MR 842766 | Zbl 0617.35036
- ,