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The Kato square root problem follows from an extrapolation property of the Laplacian. (English) Zbl 1349.35112

The authors consider the Kato square root problem for maximal accretive realizations of complex-valued elliptic systems in divergence form on a wide class of domains. They relate the solution of this problem to a regularity result for the negative Laplacian in the same setting.

MSC:

35J57 Boundary value problems for second-order elliptic systems
47A60 Functional calculus for linear operators
42B37 Harmonic analysis and PDEs