Pointwise estimates for solutions of singular quasi-linear parabolic equations

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

Pointwise estimates for solutions of singular quasi-linear parabolic equations

Vitali Liskevich ^1, and Igor I. Skrypnik ^2,

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

Abstract
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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.

Keywords: Singular parabolic equations, pointwise estimates, Wolff potential..

Mathematics Subject Classification: 35B40, 35K5.

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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