Bibliographic Details
| Title: |
H\'older stability estimates for the determination of time-independent potentials in a relativistic wave equation in an infinite waveguide |
| Authors: |
Kumar, Mandeep, Zimmermann, Philipp |
| Publication Year: |
2025 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Analysis of PDEs, 35R30, 35L05, 44A12 |
| More Details: |
The main goal of this article is to establish H\"older stability estimates for the Calder\'on problem related to a relativistic wave equation. The principal novelty of this article is that the partial differential equation (PDE) under consideration depends on three unknown potentials, namely a temporal dissipative potential $A_0$, a spatial vector potential $A$ and an external potential $\Phi$. Moreover, the PDE is posed in an infinite waveguide geometry $\Omega=\omega\times\mathbb{R}$ and not on a bounded domain. For our proof it is essential that the potentials are time-independent as a key tool in this work are pointwise estimates for the Radon transform of the vector potential $\mathcal{A}=(A_0,\mathrm{i} A)$ and external potential $\Phi$. Furthermore, the demonstrated stability estimates hold for a wide range of $H^s$ Sobolev scales and a main contribution is to explicitly determine the dependence of the involved constants and the H\"older exponent on the Sobolev exponents of the potentials $A_0,A$ and $\Phi$.
Comment: 40 pages |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2501.17308 |
| Accession Number: |
edsarx.2501.17308 |
| Database: |
arXiv |
