Abstract We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.

中文翻译：

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Ws,p(·,·)(ℝN)的浓度-致密性原理及应用

摘要 我们获得了具有可变指数的分数 Sobolev 空间的临界嵌入和集中紧致原理。作为这些结果的应用，对于一类具有变指数的关键非局部问题，我们获得了许多解的存在性，这对于常数指数情况来说甚至是新的。