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Uniqueness of continuation for semilinear elliptic equations

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  • Mourad Choulli

    (Université de Lorraine)

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.

Suggested Citation

  • Mourad Choulli, 2024. "Uniqueness of continuation for semilinear elliptic equations," Partial Differential Equations and Applications, Springer, vol. 5(4), pages 1-14, August.
    • Handle: RePEc:spr:pardea:v:5:y:2024:i:4:d:10.1007_s42985-024-00295-x
    DOI: 10.1007/s42985-024-00295-x
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    References listed on IDEAS

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    1. Mourad Bellassoued & Mourad Choulli, 2023. "Global logarithmic stability of a Cauchy problem for anisotropic wave equations," Partial Differential Equations and Applications, Springer, vol. 4(3), pages 1-44, June.
    2. Mourad Choulli, 2021. "The unique continuation property for second order evolution PDEs," Partial Differential Equations and Applications, Springer, vol. 2(5), pages 1-46, October.
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    1. Mourad Bellassoued & Mourad Choulli, 2023. "Global logarithmic stability of a Cauchy problem for anisotropic wave equations," Partial Differential Equations and Applications, Springer, vol. 4(3), pages 1-44, June.

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