We establish the higher differentiability of solutions to a class of obstacle problems for integral functionals where the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher differentiability property of the weak solution v is related to the regularity of the assigned , under a suitable Sobolev assumption on the partial map that measures the oscillation of f with respect to the x variable. The main novelty is that such assumption is independent of the dimension n and that, in the case p<=n-2, improves previous known results.

中文翻译：

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具有 Sobolev 系数的障碍问题解的正则性结果

我们为积分函数的一类障碍问题建立了更高的可微性，其中凸被积函数 f 满足关于梯度变量的 p-growth 条件。在测量 f 相对于 x 变量的振荡的部分映射上的适当 Sobolev 假设下，我们推导出弱解 v 的较高可微性属性与分配的 的规律性有关。主要的新颖之处在于这种假设与维度 n 无关，并且在 p<=n-2 的情况下，改进了以前的已知结果。