Compactness versus regularity in the calculus of variations
Compactness versus regularity in the calculus of variations
复制标题
变分计算中的紧致性与正则性
DOI：
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复制
发表时间：
2011
期刊：
影响因子：
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通讯作者：
Jan Kristensen
中科院分区：
文献类型：
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作者：
Daniel Faraco;Jan Kristensen
在本文中，我们认为在$L^p$中的紧性可以是
在分数Sobolev型空间的尺度上定量地看到。
为了适应这种观点，必须在空间的尺度上工作，
可微性的程度不是用幂来衡量的，
函数，而是由一个任意函数衰减到零，
其论点。在这种情况下，我们提供了新的$L^p$紧性
这些标准是由最近的规律性结果驱动的，
拟凸积分的极小元我们还展示了刚性
某些微分方程近似解的结果
包含遵循Riesz-Kolmogorov紧性准则。
In this note we take the view that compactness in $L^p$ can be
seen quantitatively on a scale of fractional Sobolev type spaces.
To accommodate this viewpoint one must work on a scale of spaces, where
the degree of differentiability is measured, not by a power
function, but by an arbitrary function that decays to zero with
its argument. In this context we provide new $L^p$ compactness
criteria that were motivated by recent regularity results for
minimizers of quasiconvex integrals. We also show how rigidity
results for approximate solutions to certain differential
inclusions follow from the Riesz--Kolmogorov compactness criteria.