A fairly strong stability result for parabolic quasiminimizers. Issue 8 (3rd January 2018)

• Record Type: Journal Article
• Authors: Fujishima, Yohei; Habermann, Jens; Masson, Mathias
• Is Part Of: Mathematische Nachrichten. Volume 291:Issue 8/9(2018)
• Page Start: 1269
• Page End: 1282
• Publication Date: 2018-01-03
• Subjects: parabolic equations -- parabolic quasiminimizers -- regularity -- stability -- 00‐xx; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201700018
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract: In this paper we consider parabolic Q ‐quasiminimizers related to the p ‐Laplace equation in Ω T : = 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 Ω T converge to the parabolic minimizer strongly in L p ( 0, T ; W 1, 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.