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Stability for Parabolic Quasiminimizers

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Abstract

This paper studies parabolic quasiminimizers which are solutions to parabolic variational inequalities. We show that, under a suitable regularity condition on the boundary, parabolic Q-quasiminimizers related to the parabolic p-Laplace equations with given boundary values are stable with respect to parameters Q and p. The argument is based on variational techniques, higher integrability results and regularity estimates in time. This shows that stability does not only hold for parabolic partial differential equations but it also holds for variational inequalities.

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Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University, Machikaneyama-cho 1-3, 560-8531, Toyonaka, Japan

    Yohei Fujishima

  2. Department of Mathematics, University of Erlangen, Cauerstr. 11, 91058, Erlangen, Germany

    Jens Habermann

  3. Department of Mathematics, Aalto University, P.O. Box 11100, 00076, Helsinki, Finland

    Juha Kinnunen & Mathias Masson

Authors
  1. Yohei Fujishima
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  2. Jens Habermann
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  3. Juha Kinnunen
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  4. Mathias Masson
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Corresponding author

Correspondence to Juha Kinnunen.

Additional information

This research is supported by the Academy of Finland. Part of the work was done during a visit to the Institut Mittag-Leffler (Djursholm, Sweden).

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Fujishima, Y., Habermann, J., Kinnunen, J. et al. Stability for Parabolic Quasiminimizers. Potential Anal 41, 983–1004 (2014). https://doi.org/10.1007/s11118-014-9404-y

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  • DOI: https://doi.org/10.1007/s11118-014-9404-y

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