The solution of the Kato square root problem for second order elliptic operators on R n
نویسندگان
چکیده
We prove the Kato conjecture for elliptic operators on Rn. More precisely, we establish that the domain of the square root of a uniformly complex elliptic operator L = −div (A∇) with bounded measurable coefficients in Rn is the Sobolev space H1(Rn) in any dimension with the estimate ‖ √ Lf‖2 ∼ ‖∇f‖2.
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