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A singular limit problem for the Ibragimov-Shabat equation
$1$-dimensional Harnack estimates
1. | Hacettepe University, 06800, Beytepe, Ankara, Turkey |
2. | Dipartimento di Matematica "F. Casorati”, Università di Pavia, Via Ferrata 1, 27100 Pavia |
3. | Dipartimento di Matematica e Informatica "U. Dini", Università di Firenze, viale Morgagni, 67/A, 50134, Firenze |
References:
[1] |
E. DiBenedetto, Degenerate Parabolic Equations, Universitext, Springer-Verlag, New York, 1993.
doi: 10.1007/978-0-387-94020-5. |
[2] |
E. DiBenedetto, U. Gianazza and V. Vespri, Harnack estimates for quasi-linear degenerate parabolic differential equation, Acta Mathematica, 200 (2008), 181-209.
doi: 10.1007/s11511-008-0026-3. |
[3] |
E. DiBenedetto, U. Gianazza and V. Vespri, Harnack's Inequality for Degenerate and Singular Parabolic Equations, Springer Monographs in Mathematics, Springer-Verlag, New York, 2012.
doi: 10.1007/978-1-4614-1584-8. |
[4] |
E. DiBenedetto, U. Gianazza and V. Vespri, A New Approach to the Expansion of Positivity Set of Non-negative Solutions to Certain Singular Parabolic Partial Differential Equations, Proc. Amer. Math. Soc., 138 (2010), 3521-3529.
doi: 10.1090/S0002-9939-2010-10525-7. |
[5] |
F. G. Düzgün, P. Marcellini and V. Vespri, An alternative approach to the Hoelder continuity of solutions to some elliptic equations, Nonlinear Anal., 94 (2014), 133-141.
doi: 10.1016/j.na.2013.08.018. |
[6] |
F. G. Düzgün, P. Marcellini and V. Vespri, Space expansion for a solution of an anisotropic $p$-Laplacian equation by using a parabolic approach, Riv. Mat. Univ. Parma, 5 (2014), 93-111. |
[7] |
T. Kuusi, Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), 7 (2008), 673-716.
doi: 10.2422/2036-2145.2008.4.04. |
[8] |
V. Liskevich and I. I. Skrypnik, Hölder continuity of solutions to an anisotropic elliptic equation, Nonlinear Anal., 71 (2009), 1699-1708.
doi: 10.1016/j.na.2009.01.007. |
show all references
References:
[1] |
E. DiBenedetto, Degenerate Parabolic Equations, Universitext, Springer-Verlag, New York, 1993.
doi: 10.1007/978-0-387-94020-5. |
[2] |
E. DiBenedetto, U. Gianazza and V. Vespri, Harnack estimates for quasi-linear degenerate parabolic differential equation, Acta Mathematica, 200 (2008), 181-209.
doi: 10.1007/s11511-008-0026-3. |
[3] |
E. DiBenedetto, U. Gianazza and V. Vespri, Harnack's Inequality for Degenerate and Singular Parabolic Equations, Springer Monographs in Mathematics, Springer-Verlag, New York, 2012.
doi: 10.1007/978-1-4614-1584-8. |
[4] |
E. DiBenedetto, U. Gianazza and V. Vespri, A New Approach to the Expansion of Positivity Set of Non-negative Solutions to Certain Singular Parabolic Partial Differential Equations, Proc. Amer. Math. Soc., 138 (2010), 3521-3529.
doi: 10.1090/S0002-9939-2010-10525-7. |
[5] |
F. G. Düzgün, P. Marcellini and V. Vespri, An alternative approach to the Hoelder continuity of solutions to some elliptic equations, Nonlinear Anal., 94 (2014), 133-141.
doi: 10.1016/j.na.2013.08.018. |
[6] |
F. G. Düzgün, P. Marcellini and V. Vespri, Space expansion for a solution of an anisotropic $p$-Laplacian equation by using a parabolic approach, Riv. Mat. Univ. Parma, 5 (2014), 93-111. |
[7] |
T. Kuusi, Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), 7 (2008), 673-716.
doi: 10.2422/2036-2145.2008.4.04. |
[8] |
V. Liskevich and I. I. Skrypnik, Hölder continuity of solutions to an anisotropic elliptic equation, Nonlinear Anal., 71 (2009), 1699-1708.
doi: 10.1016/j.na.2009.01.007. |
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