The Kato square root estimate with Robin boundary conditions
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 $ν\cdot A\nabla u + bu = 0$ 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.
Fields of Study & Subjects
Numerical methods in inverse problems
Nonlinear Partial Differential Equations
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 8 January 2026
- Language
- EN
- Document type
- Preprint