Laurent Bakri

Laurent Bakri
Paul Sabatier University - Toulouse III | UPS Toulouse · Institut de Mathématiques de Toulouse - IMT

Doctor

About

9
Publications
431
Reads
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95
Citations
Citations since 2016
0 Research Items
70 Citations
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201620172018201920202021202205101520
201620172018201920202021202205101520
201620172018201920202021202205101520
Additional affiliations
September 2018 - present
Paul Sabatier University - Toulouse III
Position
  • Fellow
March 2013 - February 2015
Universidad Técnica Federico Santa María
Position
  • PostDoc Position
September 2011 - August 2012
University of Tours
Position
  • ATER

Publications

Publications (9)
Data
Full-text available
Let (M, g) be a compact riemannian manifold of dimension >. We consider two Paneitz–Branson type equations with general coefficients and where A g and B g are smooth symmetric (2, 0)-tensors, >, > and ε is a small positive parameter. Under suitable assumptions, we construct solutions > to (E.1) and (E.2) which blow up at one point of the manifold w...
Article
Full-text available
We give a sharp upper bound on the vanishing order of solutions to the Schrodinger equation with C-1 electric and magnetic potentials on a compact smooth manifold. Our main result is that the vanishing order of nontrivial solutions to Delta u + V . del u + Wu = 0 is everywhere less than C (1 + parallel to W parallel to(1/2)(C1) + parallel to V para...
Article
Let (M, g) be a compact riemannian manifold of dimension n >= 5. We consider a Paneitz-Branson type equation with general coefficients Delta(2)(g)u - div(g)(A(g)du) + hu = vertical bar u vertical bar(2)*(-2-epsilon)u on M, where A(g) is a smooth symmetric (2, 0)-tensor, h is an element of C-infinity(M), 2* = 2n/n-4 and epsilon is a small positive p...
Article
Full-text available
On a closed manifold, we give a quantitative Carleman estimate on theSchrödinger operator. We then deduce quantitative uniqueness results for solutions to the Schrödinger equation using doubling estimates.Finally we investigate the sharpness of this results with respect to the electric potential.
Article
We study the possible vanishing order of solutions to Schrodinger equation in case the potential is a bounded function. We give an upper bound on compact manifold. We also show that this result is sharp.
Article
Full-text available
We give a sharp upper bound on the vanishing order of solutions to Schr\"odinger equation, in the case that the potential is of class $\mathcal{C}^1$ on a smooth compact manifold.
Article
We give an upper bound for the $(n-1)$-dimensional Hausdorff measure of the critical set of eigenfunctions of the Laplacian on compact analytic Riemannian manifolds. This is the analog of H. Donnely and C. Fefferman result on nodal set of eigenfunctions.

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