Year: 2026
Type: preprint
Abstract: We establish a global uniqueness result at the critical Sobolev regularity for the isotropic Calderón problem in all dimensions $n\ge 4$. More precisely, for every $n\ge4$ and every bounded Lipschitz domain $Ω\subset\mathbb{R}^n$, any real-valued, uniformly elliptic scalar conductivity $γ\in W^{1,n}(Ω)$ is uniquely determined by its full Dirichlet-to-Neumann map. This settles a long-standing open problem in the field. To prove uniqueness at this endpoint, we develop an averaged trace norm method, which combines complex geometrical optics with trace norm estimates averaged over wave orientations.
Source: arXiv (Cornell University)
Authors: Chen, Lu, Jiang, Yan, Liu, Hongyu, Tao, Longyue
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216362728