We establish higher differentiability results of integer order for solutions to a class of obstacle problems with nearly linear growth, provided that we assume a suitable extra integer differentiability property of Sobolev order on the gradient of the obstacle. Our results cover a large class of models for which the Lavrentiev phenomenon does not appear.

中文翻译：

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具有几乎线性增长条件的一类障碍问题的更高可微性

我们为近似线性增长的一类障碍问题建立了更高阶的整数阶微分结果，只要我们假设障碍物坡度上的Sobolev阶具有合适的额外整数微分性质。我们的结果涵盖了不会出现Lavrentiev现象的大量模型。