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So far we discussed Carleman estimates only for evolution equations. In this chapter, we derive Carleman estimates for an elliptic equation by the same method as in Chaps. 3 – 5 . Once a Carleman estimate is derived for elliptic equations, we can apply it to several problems for the elliptic equations such as conditional stability for a Cauchy problem by the same way as Sect. 4.5 of Chap. 4 , but we omit the details.

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Derivation of Carleman Estimates for Elliptic Equations

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  • 发表日期：

    2025年

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  • Masahiro Yamamoto

摘要

So far we discussed Carleman estimates only for evolution equations. In this chapter, we derive Carleman estimates for an elliptic equation by the same method as in Chaps. 3 – 5 . Once a Carleman estimate is derived for elliptic equations, we can apply it to several problems for the elliptic equations such as conditional stability for a Cauchy problem by the same way as Sect. 4.5 of Chap. 4 , but we omit the details.