Non-linear elliptic systems with measure-valued right hand side

Abstract

ABSTRACT. -We prove existence of a solution u for the nonlinear elliptic system

Regularity results for the gradient of solutions of linear elliptic systems with VMO-coefficients and L 1,λ data

“…As a matter of fact in [20] the authors consider nonlinear elliptic systems −div σ(x, u(x), Du(x)) = μ in Ω u = 0 on∂Ω…”

Gradient estimates for problems with Orlicz growth

“…Corresponding results for systems are provided in [40]. Let us refer also to some other attempts [5,7,21,12,23,28,30,43,44,46].…”

Maximal regularity via reverse Hölder inequalities for elliptic systems of n-Laplace type involving measures

“…As shown in [8], under the assumptions (H0)-(H3) and one of the conditions (i)-(iii) on the operator (see Section 2), we can construct approximating solutions u i ∈W 1,n 0 (Ω) of the regularized system − div σ(x, u i , Du i ) = f i for smooth functions f i , bounded in L 1 (Ω), with f i !µ weakly in M(Ω). It was shown in [7] (see also [8]) that we may pass to the limit i!∞ to prove the existence of a solution u of system (1. …”