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Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent

Abstract

In this paper, we prove the Hölder continuity of solutions of parabolic equations containing the p(x, t)-Laplacian. The degree p must satisfy the so-called logarithmic condition.

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Correspondence to Yu. A. Alkhutov.

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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 28, Part I, pp. 8–74, 2011.

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Alkhutov, Y.A., Zhikov, V.V. Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent. J Math Sci 179, 347–389 (2011). https://doi.org/10.1007/s10958-011-0599-9

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  • DOI: https://doi.org/10.1007/s10958-011-0599-9

Keywords

  • Parabolic Equation
  • Integral Identity
  • Integral Inequality
  • Integral Estimate
  • Regularization Operator