Abstract
For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an arbitrarily small open subset of the boundary determines the self-adjoint operator with a Dirichlet boundary condition or with a (possibly non-self-adjoint) Robin boundary condition uniquely up to unitary equivalence. These results hold for general Lipschitz domains, which can be unbounded and may have a non-compact boundary, and under weak regularity assumptions on the coefficients of the differential expression.
Original language | English |
---|---|
Article number | 035009 |
Journal | Inverse Problems |
Volume | 36 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jan 2020 |
Keywords
- Calderon problem
- Dirichlet-to-Neumann map
- elliptic differential operator
- Gelfand problem
- inverse problem
ASJC Scopus subject areas
- Theoretical Computer Science
- Signal Processing
- Applied Mathematics
- Computer Science Applications
- Mathematical Physics