Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus

Details 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

2010-12-09

arxiv.org/abs/1012.2061v1

Mathematics

Functional Analysis

31 pages, 7 pages

Scientific paper

We give 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.

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