Abstrakt
We consider a class of nonlinear non-diagonal elliptic systems with p-growth and establish the L-q-integrability for all q is an element of [p, p + 2] of any weak solution provided the corresponding right hand side belongs to the corresponding Lebesgue space and the involved elliptic operator asymptotically satisfies the p-uniform ellipticity, the so-called splitting condition and it is continuous with respect to the spatial variable. For operators satisfying the uniform p-ellipticity condition the higher integrability is known for q is an element of [p, dp/(d - 2)] and for operators having the so-called Uhlenbeck structure, the theory is valid for all q is an element of [p,infinity).
The key novelty of the paper is twofold. First, the statement uses only the information coming from the asymptotic operator and second, and more importantly, by using the splitting condition, we are able to extend the range of possible q's significantly whenever p < d - 2.