Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains

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.

accepted for publication in Inverse Problems

References in corpus (8)

• Limiting Carleman weights and anisotropic inverse problems
• Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
• The Dirichlet-to-Neumann operator via hidden compactness
• Krein's Resolvent Formula for Self-Adjoint Extensions of Symmetric Second Order Elliptic Differential Operators
• Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
• Complex spherical waves and inverse problems in unbounded domains
• Inverse problems with partial data for a magnetic Schrödinger operator in an infinite slab and on a bounded domain
• Spectral asymptotics for Robin problems with a discontinuous coefficient