A fairly strong stability result for parabolic quasiminimizers

Yohei Fujishima, Jens Habermann and Mathias Masson

Mathematische Nachrichten, 2018, vol. 291, issue 8-9, 1269-1282

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.

Date: 2018
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https://doi.org/10.1002/mana.201700018

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