Sharp Gagliardo-Nirenberg inequalities via p-Laplacian type equations. Nonlinear Dierential Equations and Applications NoDEA, p.457472, 2008. ,
Isoperimetric inequalities for eigenvalues of the Laplace operator In Fourth Summer School in Analysis and Mathematical Physics: Topics in Spectral Theory and Quantum Mechanics, Contemporary Mathematics, vol.476, p.140, 2008. ,
An extension of the Fisher information measure, Topics in Information Theory, p.113123, 1977. ,
The calculus of variations, Birkhäuser, 2004. ,
Fisher information in a Tsallis non-extensive environment, Chaos, Solitons & Fractals, vol.13, issue.3, p.451459, 2002. ,
DOI : 10.1016/S0960-0779(01)00027-3
Naudts-like duality and the extreme sher information principle, Physical Review E Pt B, vol.62, issue.5, p.74627465, 2000. ,
The Fisher information and convexity, IEEE Transactions on Information Theory, vol.14, issue.4, p.591592, 1968. ,
Existence and uniqueness of solutions for the Lane, Emden and Fowler type problem, Nonlinear Analysis: Theory, Methods & Applications, vol.72, issue.5, p.26842693, 2010. ,
DOI : 10.1016/j.na.2009.11.014
Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diusions, Journal de Mathématiques Pures et Appliquées, vol.81, issue.9, p.847875, 2002. ,
The optimal euclidean Lp-Sobolev logarithmic inequality, Journal of Functional Analysis, vol.197, issue.1, p.151161, 2003. ,
Information theoretic inequalities, IEEE Transactions on Information Theory, vol.37, issue.6, p.15011518, 1991. ,
DOI : 10.1109/18.104312
Science from Fisher Information: A Unication, 2004. ,
DOI : 10.1017/CBO9780511616907
On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics, Journal of Mathematical Physics, vol.50, issue.1, p.1330312, 2009. ,
DOI : 10.1063/1.3063640
On generalized Fisher informations and Crem??r-Rao type inequalities, Journal of Physics: Conference Series, vol.201, p.12016, 2010. ,
DOI : 10.1088/1742-6596/201/1/012016
The general optimal Lp-Euclidean logarithmic Sobolev inequality by Hamilton???Jacobi equations, Journal of Functional Analysis, vol.202, issue.2, p.591599, 2003. ,
DOI : 10.1016/S0022-1236(03)00047-8
The information generating function of a probability distribution (Corresp.), IEEE Transactions on Information Theory, vol.12, issue.1, p.7577, 1966. ,
DOI : 10.1109/TIT.1966.1053843
Robust Statistics, 2009. ,
DOI : 10.1002/0471725250
Symmetrization And Applications, World Scientic, vol.3, 2006. ,
DOI : 10.1142/6071
Logarithmic Sobolev Inequalities for Information Measures, IEEE Transactions on Information Theory, vol.55, issue.6, p.25542561, 2009. ,
DOI : 10.1109/TIT.2009.2018179
Notes on the p-Laplace equation, Report, vol.102, 2006. ,
Cram??r???Rao and Moment-Entropy Inequalities for Renyi Entropy and Generalized Fisher Information, IEEE Transactions on Information Theory, vol.51, issue.2, p.473478, 2005. ,
DOI : 10.1109/TIT.2004.840871
Moment-Entropy Inequalities for a Random Vector, IEEE Transactions on Information Theory, vol.53, issue.4, p.16031607, 2007. ,
DOI : 10.1109/TIT.2007.892780
Extensions of Fisher Information and Stam's Inequality, IEEE Transactions on Information Theory, vol.58, issue.3, pp.1319-1327, 2012. ,
DOI : 10.1109/TIT.2011.2177563
Anomalous diffusion and Tsallis statistics in an optical lattice, Physical Review A, vol.67, issue.5, p.51402, 2003. ,
DOI : 10.1103/PhysRevA.67.051402
A nonlinear singular boundary value problem in the theory of pseudoplastic uids, SIAM Journal on Applied Mathematics, vol.38, issue.2, p.275281, 1980. ,
Über Integralungleichungen zwischen einer Funktion und ihrer Ableitung ,
Generalised Exponential Families and Associated Entropy Functions, Entropy, vol.10, issue.3, p.131149, 2008. ,
DOI : 10.3390/entropy-e10030131
URL : http://doi.org/10.3390/entropy-e10030131
Abstract, Open Physics, vol.7, issue.3, p.405413, 2009. ,
DOI : 10.2478/s11534-008-0150-x
-Gaussian densities and behaviors of solutions to related diffusion equations, Journal of Physics A: Mathematical and Theoretical, vol.43, issue.3, p.35002, 2010. ,
DOI : 10.1088/1751-8113/43/3/035002
URL : https://hal.archives-ouvertes.fr/halsde-00406815
R??nyi entropies and Fisher informations as measures of nonextensivity in a Tsallis setting, Physica A: Statistical Mechanics and its Applications, vol.258, issue.3-4, pp.3-4446457, 1998. ,
DOI : 10.1016/S0378-4371(98)00272-6
Semiclassical information from deformed and escort information measures, Physica A: Statistical Mechanics and its Applications, vol.383, issue.2, p.782796, 2007. ,
DOI : 10.1016/j.physa.2007.05.009
Fisher Variational Principle and Thermodynamics, Variational and Extremum Principles in Macroscopic Systems, p.379394, 2005. ,
DOI : 10.1016/B978-008044488-8/50021-7
q-Gaussians in the porous-medium equation: stability and time evolution, The European Physical Journal B, vol.66, issue.4, p.537546, 2008. ,
DOI : 10.1140/epjb/e2008-00451-y
Some inequalities satised by the quantities of information of Fisher and Shannon, Information and Control, vol.2, issue.2, p.101112, 1959. ,
Possible generalization of Boltzmann-Gibbs statistics, Journal of Statistical Physics, vol.8, issue.1-2, p.479487, 1988. ,
DOI : 10.1007/BF01016429
Nonextensive statistical mechanics: A brief introduction, Continuum Mechanics and Thermodynamics, vol.16, issue.3, 2009. ,
DOI : 10.1007/s00161-004-0174-4
Why is the detection of q-Gaussian behavior such a common occurrence? Physica A, p.601608, 2009. ,