Sequential Lower Semi-Continuity of Non-Local Functionals
Sequential Lower Semi-Continuity of Non-Local Functionals
复制标题
非局部泛函的顺序下半连续
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Elbau
中科院分区：
文献类型：
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作者：
P. Elbau
给出了向量值Lebesgue空间上非局部泛函是弱序下半连续的一个充分必要条件。这里，非局部泛函应该具有密度的二重积分的形式，它取决于两个不同点上的函数值。
We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which depends on the function values at two different points.
The characterisation we get is essentially that the density has to be convex in one variable if we integrate over the other one with an arbitrary test function in it.
Moreover, we show that this condition is in the case of non-local functionals on real-valued Lebesgue spaces (up to some equivalence in the density) equivalent to the separate convexity of the density.