August  2013, 6(4): 1029-1042. doi: 10.3934/dcdss.2013.6.1029

Pointwise estimates for solutions of singular quasi-linear parabolic equations

1. 

Department of Mathematics, Swansea University, Swansea SA2 8PP, United Kingdom

2. 

Institute of Applied Mathematics and Mechanics, Donetsk 83114, Ukraine

Received  March 2011 Revised  September 2011 Published  December 2012

For a class of singular divergence type quasi-linear parabolicequations with a Radon measure on the right hand side we derivepointwise estimates for solutions via the nonlinear Wolffpotentials.
Citation: Vitali Liskevich, Igor I. Skrypnik. Pointwise estimates for solutions of singular quasi-linear parabolic equations. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1029-1042. doi: 10.3934/dcdss.2013.6.1029
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show all references

References:
[1]

Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat. (III), 125 (1957), 25-43.

[2]

Springer, New York, 1993. doi: 10.1007/978-1-4612-0895-2.

[3]

in "Handbook of Differential Equations. Evolution Equations" (eds. C. Dafermos and E. Feireisl), Elsevier, 1 (2004), 169-286.

[4]

Acta Mathematica, 200 (2008), 181-209. doi: 10.1007/s11511-008-0026-3.

[5]

Amer. J. Math., to appear. doi: 10.1353/ajm.2011.0023.

[6]

Lecture Notes in Math., 481, Springer, 1975.

[7]

Acta Math., 172 (1994), 137-161. doi: 10.1007/BF02392793.

[8]

Duke Math. J., 111 (2002), 1-49. doi: 10.1215/S0012-7094-02-11111-9.

[9]

Translations of Mathematical Monographs, 23 American Mathematical Society, Providence, R.I. 1967.

[10]

preprint 2010.

[11]

J. Diff. Eq., 247 (2009), 2740-2777. doi: 10.1016/j.jde.2009.08.018.

[12]

Mathematical Surveys and Monographs, 51. American Mathematical Society, Providence, RI, 1997.

[13]

Ann. of Math. (2), 168 (2008), 859-914. doi: 10.4007/annals.2008.168.859.

[14]

J. Funct. Anal., 256 (2009), 1875-1906. doi: 10.1016/j.jfa.2009.01.012.

[15]

Dokl. Akad. Nauk, 398 (2004), 458-461. (Russian)

[16]

Amer. J. Math.,124 (2002), 369-410.

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