Best constants for Gagliardo–Nirenberg inequalities and applications to nonlinear diffusions☆

By Manuel del Pino, Jean Dolbeault. 2002

296 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e09b0ce29e6c60ca1f2c974d6b44fa12975786df

Citations in the corpus

• IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL (2012, unknown): “We shall also mention that the Generalized q-Gaussian distributions appear in other elds, namely as the solution of non-linear di usion equations, or as the distributions that saturate some sharp inequalities in functional analysis [8], [9], [10], [11].”
• Hardy-Poincaré inequalities and applications to nonlinear diffusions (2007, unknown): “Le cas α ∈ (−∞,−d) repose sur la linéarisation des inégalités d’interpolation optimales obtenues dans [9].”
• The optimal Euclidean Lp-Sobolev logarithmic inequality (2003, unknown): “2 can be carried out for the functional 1 p R R jruj dx þ 1 r R R juj dx under an appropriate constraint on jjujjq: One can prove the existence of a radial minimizer using approximations on balls and an appropriate scaling argument as in [11].”
• Functional inequalities, thick tails and asymptotics for the critical mass Patlak–Keller–Segel model (2010, unknown): “14) is a particular case of the Gagliardo-Nirenberg-Sobolev (GNS) inequalities for which the sharp form was found by Del Pino and Dolbeault [20].”
• On the geometry of metric measure spaces. II (2006, unknown): “See e.g. [Ta95], [Le01], [BG99], [OV00], [ DD02 ], [CMS01], [AT04], [F¨”
• Functional Inequalities for Markov semigroups (2009, unknown): “Dolbeault in [21] to state a different form of a Sobolev inequality in R, that we shall describe.”
• The two-dimensional Keller-Segel model after blow-up (2009, unknown): “the above argument can be made rigorous with an appropriate q, proving global existence and decay to zero of %. Since the optimal constants Cq are only known for special values of q (see [ 6 ]), we cannot compute Mcrit.”
• Optimal Sobolev norms and the Lp Minkowski problem (2006, unknown): “Cordero, Nazaret, and Villani [7] extended earlier results of Aubin [2], Talenti [31], Gromov [27], Alvino, Ferone, Trombetti, and Lions [1], and Del Pino and Dolbeault [8] and established the following family of sharp L Gagliardo-Nirenberg inequalities (throughout this paper, they will be called th”
• Sharp Gagliardo–Nirenberg Inequalities via p-Laplacian Type Equations (2008, unknown): “In these cases, he recovers results previously obtained by Del-Pino and Dolbeault in [7].”
• An asymmetric affine Pólya–Szegö principle (2012, unknown): “, [3,8,20,25,26,42,58,67,71]), and the references therein).”
• Asymptotics of the Fast Diffusion Equation via Entropy Estimates (2007, unknown): “Since much is known in the case m > mc, see for instance [16, 25] and [10, 11, 13, 14, 15, 27, 36, 45] for more complete results, the main novelty of our paper is concerned with the lower range m ≤ mc, which has several interesting new features.”
• Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller–Segel equation (2011, unknown): “) More recently, the sharp constant has been found [15] for a one-parameter family of GNS inequalities for each n ≥ 2: For t > 0, let p = t+ 1, and let q = 2t.”