Partial regularity of weak solutions to nonlinear elliptic systems satisfying a Dini condition

This paper is concerned with systems of nonlinear partial differential equations -D-alpha a(i)(alpha) (x, u, delu) = b(i)(x, u, delu) (i = 1,...,N) where the coefficients a(i)(alpha) are assumed to satisfy the condition \a(i)(alpha)(x, u, xi) - a(i)(alpha) (y, nu, xi)\ less than or equal to omega (\x - y\ + \u - nu\) (1 + \xi\) for all {x,u},{y,v} is an element of Omega x R-N and all xi is an element of R-nN, and where integral (1)(o) w(t)/t dt < +<infinity> while the functions partial derivativea(i)(alpha)/partial derivative xi (j)(beta) satisfy the standard boundedness and ellipticity conditions and the function xi bar right arrow b(i) (x, u, xi) may have quadratic growth. With these assumptions we prove partial Holder continuity of bounded weak solutions u to the above system provided the usual smallness condition on parallel tou parallel to (L infinity(Omega)) is fulfilled.