Regularity for anisotropic elliptic equations with degenerate coercivity. (October 2019)

• Record Type: Journal Article
• Authors: Gao, Hongya; Leonetti, Francesco; Ren, Wei
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 493
• Page End: 505
• Publication Date: 2019-10
• Subjects: 35J70; Regularity -- Anisotropic elliptic equation -- Degenerate coercivity; 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.2019.06.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper deals with boundary value problems of the form − ∑ i = 1 n D i ( a i ( x, u ( x ), D u ( x ) ) ) = f ( x ), x ∈ Ω, u ( x ) = 0, x ∈ ∂ Ω . Assume that there exist c 1, ν, θ > 0 such that for almost all x ∈ Ω and all ( s, z ) ∈ R × R n, | a i ( x, s, z ) | ≤ c 1 1 + | z i | p i − 1, i = 1, …, n, and ν ∑ i = 1 n | z i | p i ( 1 + | s | ) θ ≤ ∑ i = 1 n a i ( x, s, z ) z i . We let f ∈ L m ( Ω ) and we derive regularity results for weak solutions.