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Harnack estimates for weak solutions to a singular parabolic equation

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Abstract

By an interpolation method, an intrinsic Harnack estimate and some sup-estimates are established for nonnegative solutions to a general singular parabolic equation.

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References

  1. Hadamard, J., Extension á l’équation de la chaleur d’un théoréme de A. Harnack, Rend. Circ. Mat. Palermo., 23, 1954, 337–346.

    Article  MathSciNet  Google Scholar 

  2. Pini, B., Sulla soluzione generalizzata diWinener per il primo problema di valori al contorno nel parabolico, Rend. Sem. Math. Padova., 23, 1954, 422–434.

    MathSciNet  MATH  Google Scholar 

  3. Moser, J., A Harnack inequality foe parabolic differential equations, Comm. Pure Appl. Math., 17, 1964, 101–134.

    Article  MathSciNet  MATH  Google Scholar 

  4. Aronson, D. G. and Serrinm, J., Local behavior of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal., 25, 1967, 81–123.

    Article  MathSciNet  MATH  Google Scholar 

  5. Trudinger, N. S., Pointwise estimates and quasilinear parabolic equations, Comm. Pure. Appl. Math., 21, 1968, 205–266.

    Article  MathSciNet  MATH  Google Scholar 

  6. Ladyzenskaja, O. A., Solonnikov, V. A. and Uralśtzeva, N. N., Linear and quasilinear equations of parabolic type, Transl. Math. Mono., 23, A. M. S., Providence, RI, 1968.

  7. Dibenedetto, E., Intrinsic Harnack type inequalities foe solutions of certain degenerate parabolic equations, Arch. Rational Mech. Anal., 100, 1988, 129–147.

    Article  MathSciNet  MATH  Google Scholar 

  8. Dibenedetto, E. and Kwong, Y. C., Harnack estimates and extinction profile for weak solutions of certain singular parabolic equations, Trans. Amer. Math. Soc., 330, 1992, 783–811.

    Article  MathSciNet  MATH  Google Scholar 

  9. Dibenedetto, E., Degenerate Parabolic Equations, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, Hong Kong, Barcelona, Budapest, 1993.

    MATH  Google Scholar 

  10. Zhao, J. and Xu, Z. H., Cauchy problem and initial traces for a doubly nonlinear degenerate parabolic equation, Sci. in China, Ser. A, 39, 1996, 73–684.

    MathSciNet  Google Scholar 

  11. Yang, S., Harnack estimates for weak solutions of equations of non-Newtonian polytropic filtration, Chin. Ann. Math., 22B(1), 2001, 63–74.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Sciences, Jimei University, Xiamen, 361021, Fujian, China

    Huashui Zhan

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  1. Huashui Zhan
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Correspondence to Huashui Zhan.

Additional information

Project supported by the Fujian Provincial Natural Science Foundation of China (No. 2009J01009) and the Natural Science Foundation of Jimei University.

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Zhan, H. Harnack estimates for weak solutions to a singular parabolic equation. Chin. Ann. Math. Ser. B 32, 397–416 (2011). https://doi.org/10.1007/s11401-011-0644-5

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  • DOI: https://doi.org/10.1007/s11401-011-0644-5

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