一类非标准增长泛函极小的C^（1，α）正则性

C￣(1,a)Regularity for Minimizers of a Functional With Nonstandard Growth Conditions

考虑一类积分泛函，它的被积函数依赖于ｕ的梯度和参数ε，并且满足某种非标准增长条件，本文证明该泛函的极小在所考虑区域Ｇ内局部有界；如果极小函数满足适当的限制条件，那么它在Ｇ内有局部Ｈｏｌｄｅｒ连续的一阶梯度，并且在Ｇ的任何紧子集上，极小函数的梯度的Ｈｏｌｄｅｒ系数和Ｈｏｌｄｅｒ指数与极小函数ｕ以及参数ε无关．

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。