We establish the higher fractional differentiability of the solutions of a problem in divergence form of the type

$$\left\{\begin{array}{cc}\hfill divA(x,Du)& ={div|F|}^{\frac{p(x)-2}{2}}F\text{in}\mathrm{\Omega },\hfill \\ \hfill u& =0\text{on}\partial \mathrm{\Omega }.\hfill \end{array}\right.$$

The main features consist in assuming that the partial map $\xi \to A(x,\xi )$ has $p(x)$‐growth, the datum F is Besov regular and both the partial map $x\to A(x,\xi )$ and the function $x\to p(x)$ are Orlicz–Besov regular.

中文翻译：

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具有可变指数的椭圆型方程解的Besov正则性

我们以类型的散度形式建立问题解的较高分数微分性

$$\left\{\begin{array}{cc}\hfill div\mathrm{一种}（X，dü）& ={div|F|}^{\frac{p（X）-2}{2}}F\text{在}\mathrm{\Omega }，\hfill \\ \hfill ü& =0\text{上}\partial \mathrm{\Omega }。\hfill \end{array}\right.$$

主要特征在于假设局部地图 $\xi \to \mathrm{一种}（X，\xi ）$ 具有 $p（X）$增长时，基准面F是Besov正则，且均为局部图$X\to \mathrm{一种}（X，\xi ）$ 和功能 $X\to p（X）$ 是Orlicz–Besov的常客。