Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 6 min ago
PreprintarXiv licencearXiv

Determining W1,n conductivities in Calderón's problem for n≥4

  • Lu Chen
  • Yan Jiang
  • Hongyu Liu
  • Longyue Tao
Open at sourcePDFDOICite

Abstract

We establish a global uniqueness result at the critical Sobolev regularity for the isotropic Calderón problem in all dimensions n≥ 4. More precisely, for every n≥4 and every bounded Lipschitz domain Ω⊂ℝn, any real-valued, uniformly elliptic scalar conductivity γ∈ W1,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.

Related

  1. Fractional Calderón problem with L∞-conductivities
    Gunther Uhlmann, Philipp Zimmermann
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. The conductivity problem with imperfect bonding interfaces and finite internal conductivities
    Hongjie Dong, Zhuolun Yang, Hanye Zhu
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Calderón problem for fractional Schrödinger operators on closed Riemannian manifolds
    Ali Feizmohammadi, Katya Krupchyk, Gunther A. Uhlmann
    Inventiones mathematicaePeer-reviewedLicence not statedFull text27 citedMathematical physicsOpenAlex
  4. A Numerical Method for the Fractional Semilinear Calderón Problem
    Mukul Dwivedi, Jesse Railo, Andreas Rupp
    arXivPreprintCC0Full textAnalysis & PDEsNumerical analysis & scientific computingarXiv
  5. The Calderón problem for near-Euclidean metrics
    Gunther Uhlmann, Yiran Wang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{chen2026determining,
  title = {{Determining $W^1,n$ conductivities in Calderón's problem for $n\geq4$}},
  author = {Lu Chen and Yan Jiang and Hongyu Liu and Longyue Tao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01529},
  eprint = {2610.01529},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01529},
}
RIS
TY  - UNPB
TI  - Determining W^1,n conductivities in Calderón's problem for n≥4
AU  - Lu Chen
AU  - Yan Jiang
AU  - Hongyu Liu
AU  - Longyue Tao
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01529
UR  - https://arxiv.org/abs/2610.01529
AB  - We establish a global uniqueness result at the critical Sobolev regularity for the isotropic Calderón problem in all dimensions n≥ 4. More precisely, for every n≥4 and every bounded Lipschitz domain Ω⊂ℝ^n, any real-valued, uniformly elliptic scalar conductivity γ∈ 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.
ER  -