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A fairly strong stability result for parabolic quasiminimizers
Author(s) -
Fujishima Yohei,
Habermann Jens,
Masson Mathias
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700018
Subject(s) - mathematics , stability (learning theory) , parabolic partial differential equation , convergence (economics) , focus (optics) , laplace transform , mathematical analysis , boundary (topology) , partial differential equation , physics , machine learning , computer science , optics , economics , economic growth
In this paper we consider parabolic Q ‐quasiminimizers related to the p ‐Laplace equation inΩ 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 inL 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.
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