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NEW GLOBAL LOGARITHMIC STABILITY RESULTS ON THE CAUCHY PROBLEM FOR ELLIPTIC EQUATIONS

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We prove the global logarithmic stability of the Cauchy problem for $H^{2}$ -solutions of an anisotropic elliptic equation in a Lipschitz domain. The result is based on existing techniques used… Click to show full abstract

We prove the global logarithmic stability of the Cauchy problem for $H^{2}$ -solutions of an anisotropic elliptic equation in a Lipschitz domain. The result is based on existing techniques used to establish stability estimates for the Cauchy problem combined with related tools used to study an inverse medium problem.

Keywords: logarithmic stability; problem; new global; cauchy problem; global logarithmic

Journal Title: Bulletin of the Australian Mathematical Society
Year Published: 2019

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