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arXiv · 2601.04678

The Kato square root estimate with Robin boundary conditions

Sebastian Bechtel·Andreas Rosén
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Abstract

We prove the Kato square root estimate for second-order divergence form elliptic operators $-div(A\nabla)$ on a bounded, locally uniform domain $D \subseteq \mathbb{R}^n$, for accretive coefficients $A \in L^\infty(D; \mathbb{C}^n)$, under the Robin boundary condition $\nu \cdot A\nabla u + bu = 0$ for a (possibly unbounded) boundary conductivity $b$. In contrast to essentially all previous estimates of Kato square root operators, no first-order approach seems possible for the Robin boundary conditions.

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Sebastian Bechtel, Andreas Rosén. 2026-01-08. The Kato square root estimate with Robin boundary conditions. https://arxiv.org/abs/2601.04678

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