We consider the inverse problem of the simultaneous identification of the coefficients σ and q of the equation from the knowledge of the Cauchy data set. We assume that , where A is a given matrix function and γ and q are unknown piecewise affine scalar functions. No sign, nor spectrum condition on q is assumed. We derive a result of global Lipschitz stability in dimension . The proof relies on the method of singular solutions and on the quantitative estimates of unique continuation.

Lipschitz stability estimate for the simultaneous recovery of two coefficients in the anisotropic Schrödinger type equation via local Cauchy data

Sonia Foschiatti
2024-01-01

Abstract

We consider the inverse problem of the simultaneous identification of the coefficients σ and q of the equation from the knowledge of the Cauchy data set. We assume that , where A is a given matrix function and γ and q are unknown piecewise affine scalar functions. No sign, nor spectrum condition on q is assumed. We derive a result of global Lipschitz stability in dimension . The proof relies on the method of singular solutions and on the quantitative estimates of unique continuation.
2024
9-set-2023
Pubblicato
https://www.sciencedirect.com/science/article/pii/S0022247X23007564
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3052941
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