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arXiv · 1311.0302

The Kato Square Root Problem for Mixed Boundary Conditions

Moritz Egert·Robert Haller-Dintelmann·Patrick Tolksdorf
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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 $\frac{1}{2}$ 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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Moritz Egert, Robert Haller-Dintelmann, Patrick Tolksdorf. 2013-11-01. The Kato Square Root Problem for Mixed Boundary Conditions. https://arxiv.org/abs/1311.0302

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