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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

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 & 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.  Google Scholar

[2]

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

[3]

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

[4]

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

[5]

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

[6]

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

[7]

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

[8]

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

[9]

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

[10]

preprint 2010.  Google Scholar

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

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