Sharp Gagliardo–Nirenberg Inequalities via p-Laplacian Type Equations

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Sharp Constants and Optimizers for a Class of Caffarelli–Kohn–Nirenberg Inequalities (2015, methodology): “Motivated by results in [23] and [1, 2, 10, 13, 22], in this paper, we will use convenient vector fields to investigate the CKN inequality in some special regions.”
IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL (2012, background): “-Gaussian distributions appearin otherﬁelds, namely as the solution ofnon-lineardiﬀusion equations, oras the distributions that saturate some sharp inequalities in functional analysis [8], [9], [10], [11]. In the literature, and in particular within nonextensive thermostatistics, several extensions ”
Sharp weighted Sobolev and Gagliardo–Nirenberg inequalities on half‐spaces via mass transport and consequences (2013, background): “In these two papers, Agueh investigated the sharp constants and optimal functions of GN inequalities involving the Lp norm of the gradient by studying a p-Laplacian-type equation.”