The Kato Square Root Problem follows from an Extrapolation Property of\n the Laplacian

2013/11/01 by Moritz Egert, Egert, Moritz, Robert Haller‐Dintelmann +3
Computer Science · Mathematics · #35J57 #42B37 #47A60 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1311.0301

openalex publication_date 2013/11/01 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

Abstract

On a domain \Ω \⊆ \ℝ^d we consider second order elliptic\nsystems in divergence form with bounded complex coefficients, realized via a\nsesquilinear form with domain V \⊆ H¹(\Ω). Under very mild\nassumptions on \Ω and V we show that the Kato Square Root Problem for\nsuch systems can be reduced to a regularity result for the fractional powers of\nthe negative Laplacian in the same geometric setting. This extends an earlier\nresult of McIntosh to non-smooth coefficients.\n

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