The solution of the Kato problem for degenerate elliptic operators with Gaussian bounds

2009/07/16 by Cruz-Uribe, D., Rios, C. · 1 citation
#35C15 #35J70 #35K65 (Secondary) #47D06 (Primary) 47N20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0907.2947

Abstract

We prove the Kato conjecture for degenerate elliptic operators in Rⁿ. More precisely, we consider the divergence form operator L_w = -1/w div (wA) grad, where w is a Muckenhoupt A₂ weight and A is a complex valued n x n matrix which is bounded and uniformly elliptic. We show that if the associated semigroup satisfies Gaussian upper bounds, then the Kato square root estimate holds.

Cited by

• Existence and uniqueness of solutions of degenerate elliptic equations with lower order terms

Related

• The Kato problem and extensions for degenerate elliptic operators of higher order in weighted spaces
• On the Kato problem for elliptic operators in non-divergence form
• The Kato problem for weighted elliptic and parabolic operators of higher order
• Weighted L^p Estimates of Kato Square Roots Associated to Degenerate Elliptic Operators
• Kato square root problem with unbounded leading coefficients