Quasilinear elliptic systems with measure data. (May 2017)

• Record Type: Journal Article
• Authors: Leonetti, Francesco; Rocha, Eugénio; Staicu, Vasile
• Is Part Of: Nonlinear analysis. Volume 154(2017)
• Page Start: 210
• Page End: 224
• Publication Date: 2017-05
• Subjects: Elliptic systems -- Existence of solutions -- Measures; 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.2016.04.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the existence of solutions of quasilinear elliptic systems involving N equations and a measure on the right hand side, with the form { − ∑ i = 1 n ∂ ∂ x i ( ∑ β = 1 N ∑ j = 1 n a i, j α, β ( x, u ) ∂ ∂ x j u β ) = μ α in Ω, u = 0 on ∂ Ω, where α ∈ { 1, …, N } is the equation index, Ω is an open bounded subset of R n, u : Ω → R N and μ is a finite Randon measure on R n with values in R N . Existence of a solution is proved for two different sets of assumptions on A . Examples are provided that satisfy our conditions, but do not satisfy conditions required on previous works on this matter.