Uniqueness of continuation for semilinear elliptic equations

Mourad Choulli ()
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Mourad Choulli: Université de Lorraine

Partial Differential Equations and Applications, 2024, vol. 5, issue 4, 1-14

Abstract: Abstract We quantify the uniqueness of continuation from Cauchy or interior data. Our approach consists in extending the existing results in the linear case. As by product, we obtain a new stability estimate in the linear case. We also show strong uniqueness of continuation and the uniqueness of continuation from a set of positive measure. These results are derived using a linearization procedure.

Keywords: Semilinear elliptic equations; Carleman inequality; Cauchy data; Interior data; Stability inequality; Uniqueness of continuation; Strong uniqueness of continuation; Continuation from a set of positive measure; 35R25; 35J61; 35J15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s42985-024-00295-x

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