Quasilinear elliptic systems with measure data. (May 2017) - Leonetti, Francesco; Rocha, Eugénio; Staicu, Vasile
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.