Year: 2025
Type: preprint
Abstract: This paper is concerned with the magnetic Laplacian $P^h (\A)=(h D+\A)^2$ in semiclassical analysis, where $h$ is a semiclassical parameter. We study the $L^2$ Neumann and Dirichlet problems for the equation $P^h(\A)u=0$ in a bounded Lipschitz domain $Ω$. Under the assumption that the magnetic field $\nabla \times \A$ is of finite type on $\overlineΩ$, we establish the nontangential maximal function estimates for $(h D+\A)u$, which are uniform for $0< h< h_0$. This extends a well-known result due to D. Jerison and C. Kenig for the Laplacian in Lipschitz domains to the magnetic Laplacian in the semiclassical setting. Our results are new even for smooth domains.
Source: arXiv (Cornell University)
Author: Shen, Zhongwei
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416682745
Cites:
Cited by:
Related to: