Remainder Terms in the Fractional Sobolev Inequality
Remainder Terms in the Fractional Sobolev Inequality
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DOI：
10.1512/iumj.2013.62.5065
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发表时间：
2013-01-01
影响因子：
1.1
通讯作者：
Weth, Tobias
中科院分区：
文献类型：
--
作者：
Chen, Shibing;Frank, Rupert L.;Weth, Tobias
证明了嵌入H-s/2（R-N）的分数阶Sobolev不等式L2 N/（N-s）（R-N），S是（0，N）的元素，通过增加一个与到最优解集的距离成比例的余项，可以使分数阶Sobolev不等式尖锐化.作为推论，我们得到了有限测度区域上支持函数在弱LN/（N-s）-范数下余项的存在性.我们的结果推广了早期的工作，为非分数的情况下，S是一个偶数。
We show that the fractional Sobolev inequality for the embedding H-s/2(R-N) hooked right arrow L2N/(N-s)(R-N), S is an element of (0, N) can be sharpened by adding a remainder term proportional to the distance to the set of optimizers. As a corollary, we derive the existence of a remainder term in the weak LN/(N-s)-norm for functions supported in a domain of finite measure. Our results generalize earlier work for the non-fractional case where S is an even integer.