Lotfi Thabouti

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Research Interests :

My research focuses on the mathematical analysis of partial differential equations and harmonic analysis, particularly in the study of unique continuation properties, Carleman estimates, and control theory. Throughout my thesis, I have concentrated on introducing global Lp Carleman estimates for elliptic boundary value problems, employing harmonic analysis techniques like Fourier analysis, the construction of the parametrix, Fourier multipliers operators and the restriction theory. By using Wolff’s osculation argument on measures in Rd, we provide a quantification of unique continuation for solutions of the Laplace operator with respect to the lower-order terms in quasi optimal Lp spaces. Building on these results, my future research aims to tackle several problems related to the optimality of unique continuation estimates, their applications to control theory and inverse problems.


I also have a strong interest in mathematical physics and I am open to working on questions related to the Cauchy problem and regularity theory.

Publications and preprints:

[2] Quantitative unique continuation for non-regular perturbations of the Laplacian

(With Pedro Caro and Sylvain Ervedoza) Preprint Novembre 2024 - [HAL]

[1] Lp Carleman estimates for elliptic boundary value problems and applications to the quantification of unique continuation

(With Belhassen Dehman and Sylvain Ervedoza) Annales Henri Lebesgue. 7 (2024), 1603-1668- [doi] - [HAL]

Talks :