標題: | Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo's lemma |
作者: | Spector, Daniel Van Schaftingen, Jean 應用數學系 Department of Applied Mathematics |
關鍵字: | Korn-Sobolev inequality;Lorentz spaces;Loomis-Whitney inequality |
公開日期: | 1-一月-2019 |
摘要: | We prove a family of Sobolev inequalities of the form parallel to u parallel to(n/Ln-1, 1(Rn, V)) <= C parallel to A(D)u parallel to(L1(Rn,E)) where A(D) : C-c(infinity)(R-n ,V) -> C-c(infinity)(R-n , E) is a vector first-order homogeneous linear differential operator with constant coefficients, a is a vector field on R-n and L-n/n-1,L- 1 (R-n) is a Lorentz space. These new inequalities imply in particular the extension of the classical Gagliardo-Nirenberg inequality to Lorentz spaces originally due to Alvino and a sharpening of an inequality in terms of the deformation operator by Strauss (Korn Sobolev inequality) on the Lorentz scale. The proof relies on a nonorthogonal application of the Loomis-Whitney inequality and Gagliardo's lemma. |
URI: | http://dx.doi.org/10.4171/RLM/854 http://hdl.handle.net/11536/152862 |
ISSN: | 1120-6330 |
DOI: | 10.4171/RLM/854 |
期刊: | RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI |
Volume: | 30 |
Issue: | 3 |
起始頁: | 413 |
結束頁: | 436 |
顯示於類別: | 期刊論文 |