The interior BMO-regularity for a weak solution of nonlinear second order elliptic systems (Q1871711)

In this paper the author studies the \(BMO\) regularity for the solution of the following nonlinear elliptic system \[ - D_\alpha\left(A_i^\alpha(Du)\right) = 0, \qquad i=1,\dots,N, \;Ns>1 \] in a bounded domain \(\Omega \subset \mathbb R^n, \;n>2\). Regarding the coefficients of the systems some suitable conditions on the continuity and the differentiability are assumed to hold. The main result of the paper is that the gradient of any solution belongs to the class \(BMO\).