Asymptotic expansions and extremals for the critical Sobolev and Gagliardo–Nirenberg inequalities on a torus
Asymptotic expansions and extremals for the critical Sobolev and Gagliardo–Nirenberg inequalities on a torus
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环面上临界 Sobolev 和 Gagliardo-Nirenberg 不等式的渐近展开和极值
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发表时间：
2010
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通讯作者：
S. Zelik
中科院分区：
文献类型：
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作者：
M. Bartuccelli;J. Deane;S. Zelik
本文全面研究了零均值周期函数的插值不等式，包括极值的存在性、渐近展开式、最佳常数、各种余项等。尽管也得到了一些关于代数情况下和不同空间维度下的最佳常数的结果，但大多数注意力都集中在二维情况下的临界（对数）Sobolev不等式上。
We present a comprehensive study of interpolation inequalities for periodic functions with zero mean, including the existence of and the asymptotic expansions for the extremals, best constants, various remainder terms, etc. Most attention is paid to the critical (logarithmic) Sobolev inequality in the two-dimensional case, although a number of results concerning the best constants in the algebraic case and different space dimensions are also obtained.