Multidimensional Opial inequalities for functions vanishing at an interior point
George A. Anastassiou; Gisèle Ruiz Goldstein; Jerome A. Goldstein
- Volume: 15, Issue: 1, page 5-15
- ISSN: 1120-6330
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topAnastassiou, George A., Goldstein, Gisèle Ruiz, and 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 15.1 (2004): 5-15. <http://eudml.org/doc/252314>.
@article{Anastassiou2004,
abstract = {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.},
author = {Anastassiou, George A., Goldstein, Gisèle Ruiz, Goldstein, Jerome A.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Integral inequalities; Opial-type multidimensional inequality; Sharp inequality; integral inequalities; sharp inequality},
language = {eng},
month = {3},
number = {1},
pages = {5-15},
publisher = {Accademia Nazionale dei Lincei},
title = {Multidimensional Opial inequalities for functions vanishing at an interior point},
url = {http://eudml.org/doc/252314},
volume = {15},
year = {2004},
}
TY - JOUR
AU - Anastassiou, George A.
AU - Goldstein, Gisèle Ruiz
AU - Goldstein, Jerome A.
TI - Multidimensional Opial inequalities for functions vanishing at an interior point
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/3//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 1
SP - 5
EP - 15
AB - 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.
LA - eng
KW - Integral inequalities; Opial-type multidimensional inequality; Sharp inequality; integral inequalities; sharp inequality
UR - http://eudml.org/doc/252314
ER -
References
top- AGARWAL, R.P. - PANG, P.Y.H., Opial inequalities with applications in differential and difference equations. Kluwer Academic Publishers, Dordrecht-Boston-London1995. Zbl0821.26013MR1340422
- BEESACK, P.R., On an integral inequality of Z. Opial. Trans. Amer. Math. Soc., 104, 1962, 479-475. Zbl0122.30102MR139706
- FLEMING, W., Functions of Several Variables. Undergraduate texts in mathematics, 2nd ed., Springer-Verlag, New York1977. Zbl0136.34301MR422527
- LEVINSON, N., On an inequality of Opial and Beesack. Proc. Amer. Math. Soc., 15, 1964, 565-566. Zbl0134.27902MR166315
- NEČAEV, I.D., Integral inequalities with gradients and derivatives. Soviet Math. Dokl., 22, 1973, 1184-1187. Zbl0288.26008
- OLECH, C., A simple proof of a certain result of Z. Opial. Ann. Polon. Math., 8, 1960, 61-63. Zbl0089.27404MR112927
- OPIAL, Z., Sur une inégalité. Ann. Polon. Math., 8, 1960, 29-32. Zbl0089.27403MR112926
- 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. Zbl0979.26011MR1804782
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