Extension of a regularity result concerning the dam problem
Gilardi, Gianni ; Luckhaus, Stephan
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 2 (1991), p. 287-296 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

One proves, in the case of piecewise smooth coefficients, that the time derivative of the solution of the so called dam problem is a measure, extending the result proved by the same authors in the case of Lipschitz continuous coefficients.

Si dimostra, nel caso di coefficienti regolari a tratti, che la derivata rispetto alla variabile temporale della soluzione del cosiddetto problema della diga è una misura, estendendo il risultato che gli stessi autori hanno già dimostrato nel caso di coefficienti lipschitziani.

Publié le : 1991-12-01
@article{RLIN_1991_9_2_4_287_0,
     author = {Gianni Gilardi and Stephan Luckhaus},
     title = {Extension of a regularity result concerning the dam problem},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {2},
     year = {1991},
     pages = {287-296},
     zbl = {0766.35083},
     mrnumber = {1152635},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1991_9_2_4_287_0}
}

Gilardi, Gianni; Luckhaus, Stephan. Extension of a regularity result concerning the dam problem. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 2 (1991) pp. 287-296. http://gdmltest.u-ga.fr/item/RLIN_1991_9_2_4_287_0/

[1] Alt, H. W. - Luckhaus, S. - Visitin, A., On nonstationary flow through porous media. Ann. Mat. Pura Appl., IV, 136, 1984, 303-316. | MR 765926 | Zbl 0552.76075

[2] Baiocchi, C. - Capelo, A., Variational and quasivariational inequalities, applications to free boundary problems. Wiley, Chichester 1983. | MR 745619 | Zbl 0551.49007

[3] Carrello, J., Uniqueness and periodic behaviour of the solution to the evolution dam problem. To appear.

[4] Carrello, J. - Gilardi, G., La vitesse de propagation dans le problème de la digue. Ann. Faculté des Sciences de Toulouse, to appear. | Zbl 0723.76094

[5] Chipot, M., Variational inequalities and flow in porous media. Springer Verlag, New York1974. | MR 747637 | Zbl 0544.76095

[6] Di Benedetto, E. - Friedman, A., Periodic behaviour for the evolutionary dam problem and related free boundary problems. Comm. on Partial Diff. Equations, 11, 1986, 1297-1377. | MR 857169 | Zbl 0624.35084

[7] Friedman, A., Variational principles and free boundary problems. Wiley, New York1982. | MR 679313 | Zbl 0564.49002

[8] Gilardi, G., A new approach to evolution free boundary problems. Comm. on Partial Diff. Equations, 4, 1979, 1099-1123; 5, 1980, 983-984. | MR 544884 | Zbl 0426.35096

[9] Gilardi, G., The support of the solution in the dam problem. Proceedings of the International colloquium on Free boundary problems: theory and applications (Montreal, Canada, 13-22/6/1990), to appear. | MR 1216385 | Zbl 0793.76091

[10] Gilardi, G. - Kroner, D., The dam problem in unbounded domains. Ann. Mat. Pura Appl., to appear. | MR 1243960 | Zbl 0787.76086

[11] Gilardi, G. - Luckhaus, S., A regularity result for the solution of the dam problem. To appear. | MR 1354795 | Zbl 0845.35136

[12] Kinderlehrer, D. - Stampacchia, G., An introduction to variational inequalities and their applications. Academic Press, New York 1980. | MR 567696 | Zbl 0457.35001

[13] Torelli, A., Su un problema di frontiera libera di evoluzione. Boll. U.M.I., (4), 11, 1975, 559-570. | MR 406069 | Zbl 0331.76058

[14] Visitin, A., Existence results for some free boundary filtration problems. Ann. Mat. Pura Appl., IV, 124, 1980, 293-320. | MR 591561 | Zbl 0445.76078