Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Inverse problems for semilinear elliptic PDE with measurements at a single point
HTML articles powered by AMS MathViewer

by Mikko Salo and Leo Tzou
Proc. Amer. Math. Soc. 151 (2023), 2023-2030
DOI: https://doi.org/10.1090/proc/16255
Published electronically: February 10, 2023

Abstract:

We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the Dirichlet-to-Neumann map measured at a single boundary point, or integrated against a fixed measure. This result is valid even when the Dirichlet data is only given on a small subset of the boundary. We also give related uniqueness results on Riemannian manifolds.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 35R30
  • Retrieve articles in all journals with MSC (2020): 35R30
Bibliographic Information
  • Mikko Salo
  • Affiliation: Department of Mathematics and Statistics, University of Jyvaskyla, Jyvaskyla, Finland
  • MR Author ID: 749335
  • ORCID: 0000-0002-3681-6779
  • Email: mikko.j.salo@jyu.fi
  • Leo Tzou
  • Affiliation: Korteweg-de Vries Institute, University of Amsterdam, Amsterdam, Netherlands
  • MR Author ID: 746423
  • Email: leo.tzou@gmail.com
  • Received by editor(s): March 15, 2022
  • Received by editor(s) in revised form: August 26, 2022
  • Published electronically: February 10, 2023
  • Additional Notes: The first author was partly supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant 284715) and by the European Research Council under Horizon 2020 (ERC CoG 770924). The second author was partly supported by Australian Research Council Discovery Projects DP190103451 and DP190103302.
  • Communicated by: Ryan Hynd
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 2023-2030
  • MSC (2020): Primary 35R30
  • DOI: https://doi.org/10.1090/proc/16255
  • MathSciNet review: 4556197