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Regularity of solutions of Degenerate Quasilinear Parabolic Equations (weighted case)

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Abstract

We establish the inner regularity of solutions and their derivatives with respect to spatial coordinates for a degenerate quasilinear parabolic equation of the second order.

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References

  1. S. Chanillo and R. L. Wheeden, “Weighted Poincaré and Sobolev inequalities and estimates for weighted Peano maximal functions,” Amer. J. Math., 107, 1191–1226 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  2. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian] Nauka, Moscow 1967.

    Google Scholar 

  3. F. Chiarenza and R. A. Serapioni, “A Harnack inequality for degenerate parabolic equations,” Coram. Part. Different. Equat., 9, 719–749 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  4. C. E. Gutierrez and R. L. Wheeden, “Harnack’s inequality for degenerate parabolic equations,” Comm. Part. Different. Equat., 16, Nos. 4–5, 745–770 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  5. E. Di Benedetto, “On the local behavior of solutions of degenerate parabolic equations with measurable coefficients,” Ann. Sc. Norm. Sup., 13, No. 3, 485–535 (1986).

    Google Scholar 

  6. E. Di Benedetto and Chen Ya-Zhe, “On the local behavior of solutions of singular parabolic equations,” Arch. Rat. Mech. Anal., 103, No. 4, 319–346 (1988).

    Google Scholar 

  7. E. Di Benedetto and A. Friedman, “Holder estimates for nonlinear degenerate parabolic systems,” J. Reine Math., 357, 1–22 (1985).

    Google Scholar 

  8. S. Leonardi and I.I. Skrypnik, Necessary Conditions for Regularity of a Boundary Point for a Degenerate Quasilinear Parabolic Equations, Preprint, Catania University, Catania (1995).

    Google Scholar 

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Skrypnik, I.I. Regularity of solutions of Degenerate Quasilinear Parabolic Equations (weighted case). Ukr Math J 48, 1099–1118 (1996). https://doi.org/10.1007/BF02390967

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  • DOI: https://doi.org/10.1007/BF02390967

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