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Hölder stability estimates for the determination of time-independent potentials in a relativistic wave equation in an infinite waveguide
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DOI：10.1088/1361-6420/ae4733.png)
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Abstract
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The main goal of this article is to establish H & ouml;lder stability estimates for the Calder & oacute;n 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 Phi. Moreover, the PDE is posed in an infinite waveguide geometry Omega=omega & times;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,iA) and external potential Phi. 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 H & ouml;lder exponent on the Sobolev exponents of the potentials A0,A and Phi.
Keywords:
relativistic wave equation
dissipation
infinite wave guide
inverse problems
stability
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2.1
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78
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