2025/01/28 by M. M. Kumar, Philipp Zimmermann, Kumar, Mandeep +1
Mathematics · Physics and Astronomy · #35L05 #35R30 #44A12 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gyrotron and Vacuum Electronics Research
paper · pdf · doi:10.48550/arxiv.2501.17308
openalex publication_date 2025/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main goal of this article is to establish Hölder stability estimates for the Calderón 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 A0, a spatial vector potential A and an external potential Φ. Moreover, the PDE is posed in an infinite waveguide geometry Ω=ω×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 A=(A0,i A) and external potential Φ. Furthermore, the demonstrated stability estimates hold for a wide range of Hs Sobolev scales and a main contribution is to explicitly determine the dependence of the involved constants and the Hölder exponent on the Sobolev exponents of the potentials A0,A and Φ.