The solution of the Kato square root problem for second order elliptic operators on Rn

• 成果类型: Article
• 署名作者: Auscher, P; Hofmann, S; Lacey, M; McIntosh, A; Tchamitchian, P
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3597201
• 发表日期: 2002
• 页码: 633-654
• 关键词: heat kernel; CONSERVATION; bounds

摘要

We prove the Kato conjecture for elliptic operators on R-n. More precisely, we establish that the domain of the square root of a uniformly complex elliptic operator L = -div (Adel) with bounded measurable coefficients in R-n is the Sobolev space H-1(R-n) in any dimension with the estimate parallel torootLfparallel to(2) similar to parallel todelfparallel to(2).