Arefinement of the Bukhgeim-Klibanov method
Analysis of PDEs
2026-03-27 v1
Abstract
In this article, we improve the classical Bukhgeim-Klibanov method presented in [1],which can be used to prove the conditional stability of inverse source problem for a hyperbolic equation from the measurement on the subboundary. A major ingredient of our proof is a novel Carleman estimate. This inequality eliminates the need to extend the solution in time, therefore simplifies the existing proofs, which is widely applicable to various evolution equations.
Keywords
Cite
@article{arxiv.2603.25205,
title = {Arefinement of the Bukhgeim-Klibanov method},
author = {Suliang Si},
journal= {arXiv preprint arXiv:2603.25205},
year = {2026}
}