Exponential Decays of Steklov Eigenfunctions for the Magnetic Laplacian

Zhongwei Shen

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arXiv · 2511.14054

Exponential Decays of Steklov Eigenfunctions for the Magnetic Laplacian

Zhongwei Shen

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Abstract

Consider the Dirichlet-to-Neumann map $\Lambda_\beta$ associated with the Schr\"odinger operator $(D+\beta \A)^2$ with a magnetic potential in a bounded Lipschitz domain $\Omega$, where $\beta>1$ is the field strength parameter. Assume that the magnetic field $\B=\nabla \times \A$ is of finite type. We show that if $\beta>\beta_0$, the ground state for $\Lambda_\beta$ decays exponentially away from a neighborhood of the subset of $\partial\Omega$, on which $\B$ vanishes to the maximal order.

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Zhongwei Shen. 2025-11-18. Exponential Decays of Steklov Eigenfunctions for the Magnetic Laplacian. https://arxiv.org/abs/2511.14054

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