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-Jan-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
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