Consider on G an integral functional of which the integrand depends on thegradient of u and on a parameter ε and satisfies certain nonstandard growth conditions。The local boundedness of the minimizer of the functional is proved. Furthermore

if theminimizer

u

satisfies suitable restrictive conditions

then it has locally Hldercontinuous fisst gradient;and on any compact suoset of G the Holder coefficient and theHolder exponent of the gradient of the minimizer are independent of u and ε

theminimizer and the parameter

respectively。