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Peer-reviewedCC BYCalculus of Variations and Partial Differential Equations

The global inverse fractional conductivity problem

  • Giovanni Covi1,2
  • Jesse Railo3,4
  • Philipp Zimmermann5,6
6 affiliations
  1. 1Institut fur Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
  2. 2University of Jyväskylä, Department of Mathematics and Statistics, Seminaarinkatu 15, FI-40014 University of Jyväskylä, PO Box 35 Finland
  3. 3Computational Engineering, School of Engineering Sciences, Lappeenranta-Lahti University of Technology LUT, Lappeenranta, Finland
  4. 4Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB3 0WB UK
  5. 5Department of Mathematics, ETH Zurich, Zürich, Switzerland
  6. 6Institute of Mathematics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
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Abstract

uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be nontrivial in the exterior of the domain and isotropic, while the data is given in the form of partial Dirichlet-to-Neumann (DN) maps measured in nondisjoint open subsets of the exterior. This can be seen as the fractional counterpart of the classical inverse conductivity problem. The proof is based on a unique continuation property (UCP) for the DN maps and a novel exterior determination method from the partial exterior DN maps, which is a nonlocal analog of the classical boundary determination method by Kohn and Vogelius. Exterior determination is achieved independently of the UCP and despite the nonlocality of the equation.

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Cite

BibTeXRIS
BibTeX
@article{covi2026global,
  title = {{The global inverse fractional conductivity problem}},
  author = {Giovanni Covi and Jesse Railo and Philipp Zimmermann},
  journal = {Calculus of Variations and Partial Differential Equations},
  year = {2026},
  month = sep,
  doi = {10.1007/s00526-026-03401-6},
  url = {https://doi.org/10.1007/s00526-026-03401-6},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - The global inverse fractional conductivity problem
AU  - Giovanni Covi
AU  - Jesse Railo
AU  - Philipp Zimmermann
PY  - 2026
DA  - 2026/09/01
JO  - Calculus of Variations and Partial Differential Equations
DO  - 10.1007/s00526-026-03401-6
UR  - https://doi.org/10.1007/s00526-026-03401-6
AB  - uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be nontrivial in the exterior of the domain and isotropic, while the data is given in the form of partial Dirichlet-to-Neumann (DN) maps measured in nondisjoint open subsets of the exterior. This can be seen as the fractional counterpart of the classical inverse conductivity problem. The proof is based on a unique continuation property (UCP) for the DN maps and a novel exterior determination method from the partial exterior DN maps, which is a nonlocal analog of the classical boundary determination method by Kohn and Vogelius. Exterior determination is achieved independently of the UCP and despite the nonlocality of the equation.
SN  - 0944-2669
SN  - 1432-0835
ER  -