| Abstrakt: |
We consider non-degenerate elliptic systems of the type -divA(x,Du)=g(x)in Ω⊂Rn, where u:Ω→RN, g∈L²(Ω,RN) and x→A(x,ξ) has derivatives in the Marcinkiewicz class Ln,∞(Ω) with sufficiently small distance to L∞(Ω). We prove that every weak solution u∈Wloc1,p(Ω,RN) of the system is such that the nonlinear expression of its gradient Vμ(Du):=(μ²+∣Du∣²)4/p-2Du is weakly differentiable with D(Vμ(Du))∈Lloc²(Ω). Then, we deduce higher differentiability properties for u itself and some higher integrability results for its gradient. [ABSTRACT FROM AUTHOR] |
