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Mean value properties and unique continuation
Stability of degenerate parabolic Cauchy problems
1. | Department of Mathematics and Statistics, P.O. Box 35, FI-40014 University of Jyväskylä, Finland, Finland |
References:
[1] |
L. Boccardo, A. Dall'Aglio, T. Gallouët and L. Orsina, Nonlinear parabolic equations with measure data,, J. Funct. Anal., 147 (1997), 237.
doi: 10.1006/jfan.1996.3040. |
[2] |
E. DiBenedetto and M. A. Herrero, On the Cauchy problem and initial traces for a degenerate parabolic equation,, Trans. Amer. Math. Soc., 314 (1989), 187.
doi: 10.2307/2001442. |
[3] |
E. DiBenedetto, Degenerate Parabolic Equations,, Universitext. Springer-Verlag, (1993).
doi: 10.1007/978-1-4612-0895-2. |
[4] |
Y. Fujishima, J. Habermann, J. Kinnunen and M. Masson, Stability for parabolic quasiminimizers,, Potential Anal. (to appear). Available at , (). Google Scholar |
[5] |
S. Kamin and J. L. Vázquez, Fundamental solutions and asymptotic behaviour for the $p$-Laplacian equation,, Rev. Mat. Iberoam., 4 (1988), 339.
doi: 10.4171/RMI/77. |
[6] |
J. Kinnunen and J. Lewis, Higher integrability for parabolic systems of $p$-Laplacian type,, Duke Math J., 102 (2000), 253.
doi: 10.1215/S0012-7094-00-10223-2. |
[7] |
J. Kinnunen and P. Lindqvist, Summability of semicontinuous supersolutions to a quasilinear parabolic equation,, Ann. Sc. Norm. Super. Pisa Cl. Sci., 4 (2005), 59.
|
[8] |
J. Kinnunen and P. Lindqvist, Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation,, Ann. Mat. Pura Appl., 185 (2006), 411.
doi: 10.1007/s10231-005-0160-x. |
[9] |
J. Kinnunen and M. Parviainen, Stability for degenerate parabolic equations,, Adv. Calc. Var., 3 (2010), 29.
doi: 10.1515/ACV.2010.002. |
[10] |
T. Kuusi and M. Parviainen, Existence for a degenerate Cauchy problem,, Manuscripta Math., 128 (2009), 213.
doi: 10.1007/s00229-008-0232-5. |
[11] |
G. Li and O. Martio, Stability of solutions of varying degenerate elliptic equations,, Indiana Univ. Math. J., 47 (1998), 873.
doi: 10.1512/iumj.1998.47.1458. |
[12] |
P. Lindqvist, Stability for the solutions of div$(|\nabla u |^{p-2}\nabla u)=f$ with varying $p$,, J. Math. Anal. Appl., 127 (1987), 93.
doi: 10.1016/0022-247X(87)90142-9. |
[13] |
P. Lindqvist, On nonlinear Rayleigh quotients,, Potential Anal., 2 (1993), 199.
doi: 10.1007/BF01048505. |
[14] |
T. Lukkari, Stability of solutions to nonlinear diffusion equations,, Submitted. Available at , (). Google Scholar |
[15] |
J. Naumann, Einführung in die Theorie parabolischer Variationsungleichungen, volume 64 of Teubner-Texte zur Mathematik,, BSB B. G. Teubner Verlagsgesellschaft, (1984).
|
[16] |
R. E. Showalter, Monotone operators in Banach space and nonlinear partial differential equations,, volume 49 of Mathematical Surveys and Monographs, (1997).
|
[17] |
J. Simon, Compact sets in the space $L^p(0,T;B)$,, Ann. Mat. Pura Appl., 146 (1987), 65.
doi: 10.1007/BF01762360. |
[18] |
J. L. Vázquez, The Porous Medium Equation-Mathematical Theory,, Oxford University Press, (2007).
|
show all references
References:
[1] |
L. Boccardo, A. Dall'Aglio, T. Gallouët and L. Orsina, Nonlinear parabolic equations with measure data,, J. Funct. Anal., 147 (1997), 237.
doi: 10.1006/jfan.1996.3040. |
[2] |
E. DiBenedetto and M. A. Herrero, On the Cauchy problem and initial traces for a degenerate parabolic equation,, Trans. Amer. Math. Soc., 314 (1989), 187.
doi: 10.2307/2001442. |
[3] |
E. DiBenedetto, Degenerate Parabolic Equations,, Universitext. Springer-Verlag, (1993).
doi: 10.1007/978-1-4612-0895-2. |
[4] |
Y. Fujishima, J. Habermann, J. Kinnunen and M. Masson, Stability for parabolic quasiminimizers,, Potential Anal. (to appear). Available at , (). Google Scholar |
[5] |
S. Kamin and J. L. Vázquez, Fundamental solutions and asymptotic behaviour for the $p$-Laplacian equation,, Rev. Mat. Iberoam., 4 (1988), 339.
doi: 10.4171/RMI/77. |
[6] |
J. Kinnunen and J. Lewis, Higher integrability for parabolic systems of $p$-Laplacian type,, Duke Math J., 102 (2000), 253.
doi: 10.1215/S0012-7094-00-10223-2. |
[7] |
J. Kinnunen and P. Lindqvist, Summability of semicontinuous supersolutions to a quasilinear parabolic equation,, Ann. Sc. Norm. Super. Pisa Cl. Sci., 4 (2005), 59.
|
[8] |
J. Kinnunen and P. Lindqvist, Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation,, Ann. Mat. Pura Appl., 185 (2006), 411.
doi: 10.1007/s10231-005-0160-x. |
[9] |
J. Kinnunen and M. Parviainen, Stability for degenerate parabolic equations,, Adv. Calc. Var., 3 (2010), 29.
doi: 10.1515/ACV.2010.002. |
[10] |
T. Kuusi and M. Parviainen, Existence for a degenerate Cauchy problem,, Manuscripta Math., 128 (2009), 213.
doi: 10.1007/s00229-008-0232-5. |
[11] |
G. Li and O. Martio, Stability of solutions of varying degenerate elliptic equations,, Indiana Univ. Math. J., 47 (1998), 873.
doi: 10.1512/iumj.1998.47.1458. |
[12] |
P. Lindqvist, Stability for the solutions of div$(|\nabla u |^{p-2}\nabla u)=f$ with varying $p$,, J. Math. Anal. Appl., 127 (1987), 93.
doi: 10.1016/0022-247X(87)90142-9. |
[13] |
P. Lindqvist, On nonlinear Rayleigh quotients,, Potential Anal., 2 (1993), 199.
doi: 10.1007/BF01048505. |
[14] |
T. Lukkari, Stability of solutions to nonlinear diffusion equations,, Submitted. Available at , (). Google Scholar |
[15] |
J. Naumann, Einführung in die Theorie parabolischer Variationsungleichungen, volume 64 of Teubner-Texte zur Mathematik,, BSB B. G. Teubner Verlagsgesellschaft, (1984).
|
[16] |
R. E. Showalter, Monotone operators in Banach space and nonlinear partial differential equations,, volume 49 of Mathematical Surveys and Monographs, (1997).
|
[17] |
J. Simon, Compact sets in the space $L^p(0,T;B)$,, Ann. Mat. Pura Appl., 146 (1987), 65.
doi: 10.1007/BF01762360. |
[18] |
J. L. Vázquez, The Porous Medium Equation-Mathematical Theory,, Oxford University Press, (2007).
|
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