We consider the Dirichlet problem for an elliptic multivalued maximal monotone operator $ {\mathcal A}_\varepsilon $ satisfying growth estimates of power type with a variable exponent. This exponent $ p_\varepsilon(x) $ and also the symbol of the operator $ {\mathcal A}_\varepsilon $ oscillate with a small period $ \varepsilon $ with respect to the space variable $ x $. We prove a homogenization result for this problem.

中文翻译：

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具有可变增长指数的多值单调算子的均质化

我们考虑椭圆型多值最大单调算子$ {\数学A} _ \ varepsilon $的Dirichlet问题，该变量满足幂类型具有可变指数的增长估计。指数$ p_ \ varepsilon（x）$以及运算符$ {\数学A} _ \ varepsilon $的符号相对于空间变量$ x $都有一个小周期$ \ varepsilon $振荡。我们证明了该问题的均质化结果。