Strichartz estimates for Schrödinger equations with variable coefficients
Mémoires de la Société Mathématique de France, no. 101-102 (2005), 214 p.

We prove the (local in time) Strichartz estimates (for the full range of parameters given by the scaling unless the end point) for asymptotically flat and non trapping perturbations of the flat Laplacian in n , n2. The main point of the proof, namely the dispersion estimate, is obtained in constructing a parametrix. The main tool for this construction is the use of the FBI transform.

On démontre les inégalités de Strichartz (locales en temps) pour l’ensemble des indices donnés par l’invariance d’échelle (sauf le point final) pour des perturbations asymptotiquement plates et non captantes du laplacien usuel de n , n2. Le point principal de la preuve, à savoir l’estimation de dispersion, est obtenu en construisant une paramétrixe. L’outil principal de cette construction est la théorie de la transformation de FBI construite par Sjöstrand.

DOI : https://doi.org/10.24033/msmf.414
Classification:  35A17,  35A22,  35Q40,  35Q55
Keywords: Strichartz estimates, Schrödinger equations, dispersive estimates, FBI transform, Sjöstrand’s theory
@book{MSMF_2005_2_101-102__1_0,
     author = {Robbiano, Luc and Zuily, Claude},
     title = {Strichartz estimates for Schr\"odinger equations with variable coefficients},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {101-102},
     year = {2005},
     doi = {10.24033/msmf.414},
     zbl = {1097.35002},
     mrnumber = {2193021},
     language = {en},
     url = {http://www.numdam.org/item/MSMF_2005_2_101-102__1_0}
}
Robbiano, Luc; Zuily, Claude. Strichartz estimates for Schrödinger equations with variable coefficients. Mémoires de la Société Mathématique de France, Serie 2, , no. 101-102 (2005), 214 p. doi : 10.24033/msmf.414. http://www.numdam.org/item/MSMF_2005_2_101-102__1_0/

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