Stable determination of the potential for the Helmholtz equation in the high frequency limit from boundary measurements

2025/01/18 by Choulli, Mourad, Takase, Hiroshi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.10751

Abstract

We establish a triple logarithmic stability estimate of determining the potential in a Helmholtz equation from a partial Dirichlet-to-Neumann map in the high frequency limit. This estimate is proved under the assumption that the potential is known near the boundary of a domain when the dimension is greater than or equal to 3. In addition, we show a triple logarithmic stability for an interior impedance problem.

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