Estimations de Carleman $L^p$ pour des problèmes au bord elliptiques et applications à la quantification du prolongement unique
DEHMAN, Belhassen
Université de Tunis El Manar, Faculté des Sciences de Tunis, 2092 El Manar & Ecole Nationale d'Ingénieurs de Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia.
Université de Tunis El Manar, Faculté des Sciences de Tunis, 2092 El Manar & Ecole Nationale d'Ingénieurs de Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia.
DEHMAN, Belhassen
Université de Tunis El Manar, Faculté des Sciences de Tunis, 2092 El Manar & Ecole Nationale d'Ingénieurs de Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia.
< Leer menos
Université de Tunis El Manar, Faculté des Sciences de Tunis, 2092 El Manar & Ecole Nationale d'Ingénieurs de Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia.
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Document de travail - Pré-publication
Este ítem está publicado en
2023-06-28
Resumen en inglés
The aim of this work is to prove global $L^p$ Carleman estimates for the Laplace operator in dimension $d \geq 3$. Our strategy relies on precise Carleman estimates in strips, and a suitable gluing of local and boundary ...Leer más >
The aim of this work is to prove global $L^p$ Carleman estimates for the Laplace operator in dimension $d \geq 3$. Our strategy relies on precise Carleman estimates in strips, and a suitable gluing of local and boundary estimates obtained through a change of variables. The delicate point and most of the work thus consists in proving Carleman estimates in the strip with a linear weight function for a second order operator with coefficients depending linearly on the normal variable. This is done by constructing an explicit parametrix for the conjugated operator, which is estimated through the use of Stein Tomas restriction theorems. As an application, we deduce quantified versions of the unique continuation property for solutions of $\Delta u = V u + W_1 \cdot \nabla u + \div(W_2 u)$ in terms of the norms of $V$ in $L^{q_0}(\Omega)$, of $W_1$ in $L^{q_1}(\Omega)$ and of $W_2$ in $L^{q_2}(\Omega)$ for $q_0 \in (d/2, \infty]$ and $q_1$ and $q_2$ satisfying either $q_1, \, q_2 > (3d-2)/2$ and $1/q_1 + 1/q_2< 4 (1-1/d)/(3d-2)$, or $q_1, \, q_2 > 3d/2$.< Leer menos
Palabras clave en inglés
Carleman estimates
boundary value problem
elliptic equations
Fourier restriction theorems
Proyecto ANR
Nouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux - ANR-20-CE40-0009
Orígen
Importado de HalCentros de investigación