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Almost everywhere Hölder continuity of gradients to non-diagonal parabolic systems

Abstract

We present a local almost everywhere C 1,α-regularity result for a general class of p-nonlinear non-diagonal parabolic systems. The main part of the considered systems depends on space-time variable, solution and symmetric part of the gradient of solution. To obtain our result, we adapt for the symmetric-gradient case techniques developed for the full-gradient case by Duzaar, Mingione and coauthors.

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Correspondence to Jan Burczak.

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Supported by the International Ph.D. Projects Programme of Foundation for Polish Science within the Innovative Economy Operational Programme 2007–2013. Partially supported by the National Science Centre (NCN) grant no. 2011/01/N/ST1/05411.

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Burczak, J. Almost everywhere Hölder continuity of gradients to non-diagonal parabolic systems. manuscripta math. 144, 51–90 (2014). https://doi.org/10.1007/s00229-013-0640-z

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  • DOI: https://doi.org/10.1007/s00229-013-0640-z

Mathematics Subject Classification (2000)

  • MSC 35K55
  • MSC 35B65
  • MSC 35K92