The Kato Square Root Problem for Mixed Boundary Conditions

2013/11/01 by Egert, Moritz, Haller-Dintelmann, Robert, Tolksdorf, Patrick · 1 citation
#35J05 #35J57 #46E35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1311.0302

Abstract

We consider the negative Laplacian subject to mixed boundary conditions on a bounded domain. We prove under very general geometric assumptions that slightly above the critical exponent (1)/(2) its fractional power domains still coincide with suitable Sobolev spaces of optimal regularity. In combination with a reduction theorem recently obtained by the authors, this solves the Kato Square Root Problem for elliptic second order operators and systems in divergence form under the same geometric assumptions.

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• Equivalent Characterizations and Applications of Fractional Sobolev Spaces with Partially Vanishing Traces on (ε,δ,D)-Domains Supporting D-Adapted Fractional Hardy Inequalities

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