We consider a wide class of functionals with the property of changing their growth and ellipticity properties according to the modulating coefficients in the framework of Musielak–Orlicz spaces. In particular, we provide an optimal condition on the modulating coefficient to establish the Hölder regularity and Harnack inequality for quasiminimizers of the generalized double phase functional with $\left(G,H\right)$-growth for two Young functions $G$ and $H$.

中文翻译：

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广义双相泛函的正则结果

我们考虑一类广泛的函数，这些函数具有根据Musielak-Orlicz空间框架中的调制系数来改变其增长和椭圆性的特性。特别是，我们为调制系数提供了一个最佳条件，以建立广义双相泛函拟拟器的Hölder正则性和Harnack不等式。$（G，H）$-两个Young函数的增长 $G$ 和 $H$。