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

作者：Bartuccelli Michele^*; Deane Jonathan; Zelik Sergey

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2013, 143(3): 445-482.

DOI：10.1017/S0308210511000473

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.

• 出版日期2013-6