Very weak solutions of subquadratic parabolic systems with non-standard p(x, t)-growth. (June 2017)

• Record Type: Journal Article
• Authors: Li, Qifan
• Is Part Of: Nonlinear analysis. Volume 156(2017)
• Page Start: 17
• Page End: 41
• Publication Date: 2017-06
• Subjects: Parabolic p-Laplacian -- Non-standard growth condition -- Higher integrability; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.02.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The aim of this paper is to establish a higher integrability result for very weak solutions of certain parabolic systems whose model is the parabolic p ( x, t ) -Laplacian system. Under assumptions on the exponent function p : Ω T = Ω × ( 0, T ) → ( 2 n n + 2, 2 ], it is shown that any very weak solution u : Ω T → R N with | D u | p ( ⋅ ) ( 1 − ε ) ∈ L 1 ( Ω T ) belongs to the natural energy spaces, i.e. | D u | p ( ⋅ ) ∈ L loc 1 ( Ω T ), provided ε > 0 is small enough. This extends the main result of Bögelein and Li (2014) to the subquadratic case.