標題: Best constants for two families of higher order critical Sobolev embeddings
作者: Shafrir, Itai
Speetor, Daniel
應用數學系
Department of Applied Mathematics
關鍵字: Sobolev embedding;Critical exponent;Best constant
公開日期: 1-Dec-2018
摘要: In this paper we obtain the best constants in some higher order Sobolev inequalities in the critical exponent. These inequalities can be separated into two types: those that embed into L-infinity(R-N) and those that embed into slightly larger target spaces. Concerning the former, we show that for k is an element of{1,..., N - 1}, N - k even, one has an optimal constant c(k) > 0 such that parallel to u parallel to L-infinity <= c(k) integral vertical bar del(k)(-Delta)((N- k)/2)u vertical bar for all u is an element of C-c(infinity) (R-N) (the case k = N was handled in Shafrir, 2018). Meanwhile the most significant of the latter is a variation of D. Adams' higher order inequality of J. Moser: For Omega subset of R-N, m is an element of N and p = N/m, there exists A > 0 and optimal constant beta(0) > 0 such that integral(Omega) exp(beta(0)vertical bar u vertical bar(p')) <= A vertical bar Omega vertical bar for all u such that parallel to del(m)u parallel to(Lp(Omega)) <= 1, where parallel to del(m)u parallel to(Lp(Omega)) is the traditional seminorm on the space W-m,W-p(Omega). (C) 2018 Elsevier Ltd. All rights reserved.
URI: http://dx.doi.org/10.1016/j.na.2018.04.027
http://hdl.handle.net/11536/148397
ISSN: 0362-546X
DOI: 10.1016/j.na.2018.04.027
期刊: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume: 177
起始頁: 753
結束頁: 769
Appears in Collections:Articles