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A fairly strong stability result for parabolic quasiminimizers

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  • Yohei Fujishima
  • Jens Habermann
  • Mathias Masson

Abstract

In this paper we consider parabolic Q†quasiminimizers related to the p†Laplace equation in ΩT:=Ω×(0,T). In particular, we focus on the stability problem with respect to the parameters p and Q. It is known that, if Q→1, then parabolic quasiminimizers with fixed initial†boundary data on ΩT converge to the parabolic minimizer strongly in Lp(0,T;W1,p(Ω)) under suitable further structural assumptions. Our concern is whether or not we can obtain even stronger convergence. We will show a fairly strong stability result.

Suggested Citation

  • Yohei Fujishima & Jens Habermann & Mathias Masson, 2018. "A fairly strong stability result for parabolic quasiminimizers," Mathematische Nachrichten, Wiley Blackwell, vol. 291(8-9), pages 1269-1282, June.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:8-9:p:1269-1282
    DOI: 10.1002/mana.201700018
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