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Global higher integrability for parabolic quasiminimizers in metric measure spaces

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Abstract

We prove higher integrability up to the boundary for minimal p-weak upper gradients of parabolic quasiminimizers in metric measure spaces related to the heat equation. We assume the underlying metric measure space to be equipped with a doubling measure and to support a weak Poincaré inequality. The boundary of the domain is assumed to satisfy a regularity condition.

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Authors and Affiliations

  1. Department of Mathematics, Aalto University, P.O. BOX 11000, FI-00076, Aalto, Finland

    Mathias Masson

  2. Department of Mathematics and Statistics, University of Jyväskylä, P.O.Box 35 (MaD), FI-40014, Jyväskylä, Finland

    Mikko Parviainen

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  1. Mathias Masson
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  2. Mikko Parviainen
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Correspondence to Mathias Masson.

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Masson, M., Parviainen, M. Global higher integrability for parabolic quasiminimizers in metric measure spaces. JAMA 126, 307–339 (2015). https://doi.org/10.1007/s11854-015-0019-z

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  • DOI: https://doi.org/10.1007/s11854-015-0019-z

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