| Přispěvatelé: |
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., Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux, UMR 5251, Université de Bordeaux, CNRS, Bordeaux INP, F-33400 Talence, France & Faculté des sciences de Tunis, Université de Tunis El Manar, 2092 El Manar, Tunisia, PHC Utique 46359ZJ, code CMCU: 21G1502 |
| Popis: |
The aim of this work is to prove global L p Carleman estimates for the Laplace operator in dimension d 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 ∆u = V u+W1•∇u+div (W2u) in terms of the norms of V in L q 0 (Ω), of W1 in L q 1 (Ω) and of W2 in L q 2 (Ω) for q0 ∈ (d/2, ∞] and q1 and q2 satisfying either q1, q2 > (3d − 2)/2 and 1/q1 + 1/q2 < 4(1 − 1/d)/(3d − 2), or q1, q2 > 3d/2. |
