For nonautonomous, nonuniformly elliptic integrals with so-called (p, q)-growth conditions, we show a general interpolation property allowing to get basic higher integrability results for Hölder continuous minimizers under improved bounds for the gap q/p. For this we introduce a new method, based on approximating the original, local functional, with mixed local/nonlocal functionals, and allowing for suitable estimates in fractional Sobolev spaces.

中文翻译：

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非自治积分的插值间隙界限

对于具有所谓 ( p ,  q ) 增长条件的非自治、非均匀椭圆积分，我们展示了一个通用的插值属性，允许在间隙q / p 的改进边界下获得 Hölder 连续极小值的基本更高的可积性结果。为此，我们引入了一种新方法，基于近似原始局部泛函，混合局部/非局部泛函，并允许在分数 Sobolev 空间中进行适当的估计。