Multidimensional Opial inequalities for functions vanishing at an interior point
Anastassiou, George A. ; Goldstein, Gisèle Ruiz ; Goldstein, Jerome A.
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004), p. 5-15 / Harvested from Biblioteca Digitale Italiana di Matematica
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In this paper we generalize Opial inequalities in the multidimensional case over balls. The inequalities carry weights and are proved to be sharp. The functions under consideration vanish at the center of the ball.

In questo lavoro si generalizzano alcune disuguaglianze di Opial su palle al caso multidimensionale. Si dimostra che tali disuguaglianze, che contengono pesi, sono ottimali. Le funzioni considerate si annullano al centro della palla.

Publié le : 2004-03-01
@article{RLIN_2004_9_15_1_5_0,
     author = {George A. Anastassiou and Gis\`ele Ruiz Goldstein and Jerome A. Goldstein},
     title = {Multidimensional Opial inequalities for functions vanishing at an interior point},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {15},
     year = {2004},
     pages = {5-15},
     zbl = {1072.26006},
     mrnumber = {2102751},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2004_9_15_1_5_0}
}

Anastassiou, George A.; Goldstein, Gisèle Ruiz; Goldstein, Jerome A. Multidimensional Opial inequalities for functions vanishing at an interior point. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004) pp. 5-15. http://gdmltest.u-ga.fr/item/RLIN_2004_9_15_1_5_0/

[1] Agarwal, R.P. - Pang, P.Y.H., Opial inequalities with applications in differential and difference equations. Kluwer Academic Publishers, Dordrecht-Boston-London 1995. | MR 1340422 | Zbl 0821.26013

[2] Beesack, P.R., On an integral inequality of Z. Opial. Trans. Amer. Math. Soc., 104, 1962, 479-475. | MR 139706 | Zbl 0122.30102

[3] Fleming, W., Functions of Several Variables. Undergraduate texts in mathematics, 2nd ed., Springer-Verlag, New York1977. | MR 422527 | Zbl 0136.34301

[4] Levinson, N., On an inequality of Opial and Beesack. Proc. Amer. Math. Soc., 15, 1964, 565-566. | MR 166315 | Zbl 0134.27902

[5] Nečaev, I.D., Integral inequalities with gradients and derivatives. Soviet Math. Dokl., 22, 1973, 1184-1187. | Zbl 0288.26008

[6] Olech, C., A simple proof of a certain result of Z. Opial. Ann. Polon. Math., 8, 1960, 61-63. | MR 112927 | Zbl 0089.27404

[7] Opial, Z., Sur une inégalité. Ann. Polon. Math., 8, 1960, 29-32. | MR 112926 | Zbl 0089.27403

[8] Troy, W.C., On the Opial-Olech-Beesack inequalities. USA-Chile Workshop on Nonlinear Analysis. Electron. J. Diff. Eqns., Conference, 06, 2001, 297-301. http://ejde.math.swt.edu or http://ejde.math.unt.edu. | MR 1804782 | Zbl 0979.26011