H\'older stability estimates for the determination of time-independent potentials in a relativistic wave equation in an infinite waveguide

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
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