Estimates of weighted Hölder norms of the solutions to a parabolic boundary value problem in an initially degenerate domain

Antonio Fasano; Vsevolod Solonnikov

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2002)

  • Volume: 13, Issue: 1, page 23-41
  • ISSN: 1120-6330

Abstract

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A-priori estimates in weighted Hölder norms are obtained for the solutions of a one- dimensional boundary value problem for the heat equation in a domain degenerating at time t = 0 and with boundary data involving simultaneously the first order time derivative and the spatial gradient.

How to cite

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Fasano, Antonio, and Solonnikov, Vsevolod. "Estimates of weighted Hölder norms of the solutions to a parabolic boundary value problem in an initially degenerate domain." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 13.1 (2002): 23-41. <http://eudml.org/doc/252406>.

@article{Fasano2002,
abstract = {A-priori estimates in weighted Hölder norms are obtained for the solutions of a one- dimensional boundary value problem for the heat equation in a domain degenerating at time t = 0 and with boundary data involving simultaneously the first order time derivative and the spatial gradient.},
author = {Fasano, Antonio, Solonnikov, Vsevolod},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Heat equation; Boundary value problems of higher order; A-priori estimates in weighted Hölder spaces; heat equation; boundary value problems of higher order; a-priori estimates in weighted Hölder spaces},
language = {eng},
month = {3},
number = {1},
pages = {23-41},
publisher = {Accademia Nazionale dei Lincei},
title = {Estimates of weighted Hölder norms of the solutions to a parabolic boundary value problem in an initially degenerate domain},
url = {http://eudml.org/doc/252406},
volume = {13},
year = {2002},
}

TY - JOUR
AU - Fasano, Antonio
AU - Solonnikov, Vsevolod
TI - Estimates of weighted Hölder norms of the solutions to a parabolic boundary value problem in an initially degenerate domain
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2002/3//
PB - Accademia Nazionale dei Lincei
VL - 13
IS - 1
SP - 23
EP - 41
AB - A-priori estimates in weighted Hölder norms are obtained for the solutions of a one- dimensional boundary value problem for the heat equation in a domain degenerating at time t = 0 and with boundary data involving simultaneously the first order time derivative and the spatial gradient.
LA - eng
KW - Heat equation; Boundary value problems of higher order; A-priori estimates in weighted Hölder spaces; heat equation; boundary value problems of higher order; a-priori estimates in weighted Hölder spaces
UR - http://eudml.org/doc/252406
ER -

References

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  1. Comparini, E. - Gianni, R. - Mannucci, P., A filtration problem in a composite porous material with two free boundaries. Advances in Math. Sc. and Appl., 11, 2001. Zbl1006.76094MR1907459
  2. Fasano, A., A one-dimensional flow problem in porous media with hydrophile granules. Math. Meth. Appl. Sci., 22, 1999, 605-617. Zbl0921.76167MR1682914DOI10.1002/(SICI)1099-1476(19990510)22:7<605::AID-MMA55>3.3.CO;2-O
  3. Fasano, A., Some two-scale processes involving parabolic equations. In: I. Athanasopoulos - G. Makrakis - J. Rodrigues (eds.), Free Boundary Problems, Theory and Applications. CRC Press, 1999, 39-50. Zbl0935.35180MR1702134
  4. Fasano, A., Porous media with hydrophile granules. In: A. Fasano (ed.), Complex Flows in Industrial Processes. MSSET Birkhäuser, Chapt. 10, 2000, 307-332. Zbl0943.76080MR1738017
  5. Fasano, A. - Solonnikov, V.A., On one-dimensional unsaturated flow in a porous medium with hydrophile grains. Functional Differential Equations, 8, 2001, 195-224. Zbl1062.76051MR1949999
  6. Ladyzhenskaya, O.A. - Solonnikov, V.A. - Ural'ceva, N.N., Linear and Quasilinear Equations of Parabolic Type. Trans. Math. Monographs, vol. 23, American Mathematical Society, 1988. Zbl0164.12302

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