The Solution of the Kato Problem for Divergence Form Elliptic Operators with Gaussian Heat Kernel Bounds

Abstract

Abstract of "The Solution of the Kato Problem for Divergence Form Elliptic Operators with Gaussian Heat Kernel Bounds" by Lacey, Hofman and McIntosh. We solve the square square root problem of Kato for elliptic operators L in divergence form with bounded measurable complex coefficients provided they satisfy Gaussian heat kernel bounds. More precisely, we establish that the domain of the square root of L is the Sobolev space H (Rn) and that the estimate || square root of L [function] ||2 ~||\nabla [function]||2 holds. Show more