Extension of a regularity result concerning the dam problem

Gianni Gilardi; Stephan Luckhaus

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 4, page 287-296
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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Gilardi, Gianni, and 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 2.4 (1991): 287-296. <http://eudml.org/doc/244207>.

@article{Gilardi1991,
abstract = {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.},
author = {Gilardi, Gianni, Luckhaus, Stephan},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Regularity; Porous media; Non negative subharmonic functions; porous media; nonnegative subharmonic functions; Dirichlet boundary points; Neumann boundary points; regularity; piecewise smooth coefficients},
language = {eng},
month = {12},
number = {4},
pages = {287-296},
publisher = {Accademia Nazionale dei Lincei},
title = {Extension of a regularity result concerning the dam problem},
url = {http://eudml.org/doc/244207},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Gilardi, Gianni
AU - Luckhaus, Stephan
TI - Extension of a regularity result concerning the dam problem
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/12//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 4
SP - 287
EP - 296
AB - 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.
LA - eng
KW - Regularity; Porous media; Non negative subharmonic functions; porous media; nonnegative subharmonic functions; Dirichlet boundary points; Neumann boundary points; regularity; piecewise smooth coefficients
UR - http://eudml.org/doc/244207
ER -

References

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  1. ALT, H. W. - LUCKHAUS, S. - VISITIN, A., On nonstationary flow through porous media. Ann. Mat. Pura Appl., IV, 136, 1984, 303-316. Zbl0552.76075MR765926DOI10.1007/BF01773387
  2. BAIOCCHI, C. - CAPELO, A., Variational and quasivariational inequalities, applications to free boundary problems. Wiley, Chichester1983. Zbl0551.49007MR745619
  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. Zbl0723.76094
  5. CHIPOT, M., Variational inequalities and flow in porous media. Springer Verlag, New York1974. Zbl0544.76095MR747637DOI10.1007/978-1-4612-1120-4
  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. Zbl0624.35084MR857169DOI10.1080/03605308608820466
  7. FRIEDMAN, A., Variational principles and free boundary problems. Wiley, New York1982. Zbl0564.49002MR679313
  8. GILARDI, G., A new approach to evolution free boundary problems. Comm. on Partial Diff. Equations, 4, 1979, 1099-1123; 5, 1980, 983-984. Zbl0426.35096MR544884DOI10.1080/03605307908820122
  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. Zbl0793.76091MR1216385
  10. GILARDI, G. - KRONER, D., The dam problem in unbounded domains. Ann. Mat. Pura Appl., to appear. Zbl0787.76086MR1243960DOI10.1007/BF01759326
  11. GILARDI, G. - LUCKHAUS, S., A regularity result for the solution of the dam problem. To appear. Zbl0845.35136MR1354795DOI10.1016/0362-546X(94)00183-I
  12. KINDERLEHRER, D. - STAMPACCHIA, G., An introduction to variational inequalities and their applications. Academic Press, New York1980. Zbl0457.35001MR567696
  13. TORELLI, A., Su un problema di frontiera libera di evoluzione. Boll. U.M.I., (4), 11, 1975, 559-570. Zbl0331.76058MR406069
  14. VISITIN, A., Existence results for some free boundary filtration problems. Ann. Mat. Pura Appl., IV, 124, 1980, 293-320. Zbl0445.76078MR591561DOI10.1007/BF01795398

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