Abstract
The principle objective of this first chapter is to establish a stability estimate for the Cauchy problem. We use a method built on a Carleman inequality which serves to propagate the local \(L^2\) norm of solutions and their gradients by means of three-ball inequalities.
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References
A.L. Bukhgeim, Extension of solutions of elliptic equations from discrete sets. J. Inverse Ill-Posed Probl. 1(1), 17–32 (1993)
D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edn. (Springer, Berlin, 1983)
M. Choulli, Une Introduction Aux Problèmes Inverses Elliptiques et Paraboliques, vol. 65 (SMAI-Springer, Berlin, 2009)
M. Choulli, Analyse Fonctionnelle: Équations aux Dérivées Partielles (Vuibert, Paris, 2013)
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Choulli, M. (2016). Uniqueness of Continuation and Cauchy Problems. In: Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-33642-8_2
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DOI: https://doi.org/10.1007/978-3-319-33642-8_2
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