Caffarelli-Kohn-Nirenberg inequalities with remainder terms

By Zhi-Qiang Wang, Michel Willem. 2003

106 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/024e91dd1874f855ab168ad2e7305bb0c00376e3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Nguyen Huong Lam
2. G. Lu
3. I. Peral
4. Shuangjie Peng
5. Changshou Lin
6. Alexandru Kristály
7. Boumediene Abdellaoui
8. Thomas Bartsch

In Computational Theory and Mathematics

1. Nguyen Huong Lam
2. G. Lu
3. I. Peral
4. Boumediene Abdellaoui
5. Thomas Bartsch
6. Zhi-Qiang Wang
7. Changshou Lin
8. Alexandru Kristály

In Mathematical Physics

1. Nguyen Huong Lam
2. G. Lu
3. Shuangjie Peng
4. Zhi-Qiang Wang
5. Thomas Bartsch
6. Changshou Lin
7. I. Peral
8. Boumediene Abdellaoui

Citations in the corpus

• Some improved Caffarelli-Kohn-Nirenberg inequalities (2005, methodology): “where 1 0, for some positive constant ρ(N, p, q, γ). Also we give an alternative proof of the optimal improved inequality for p =2 by Wang-Willem in [ 16 ].”
• Nonlinear schrodinger equations with unbounded and decaying radial potentials (2007, unknown): “([28]) Let N = 2.”
• Bessel pairs and optimal Hardy and Hardy–Rellich inequalities (2011, result): “Our results here include in addition those proved by Wang and Willem [ 35 ] in the case where a < n−2 2 and W (r ) =”
• Sharp Constants and Optimizers for a Class of Caffarelli–Kohn–Nirenberg Inequalities (2015, background): “In [35], Wang and Willem studied the compactness of all maximizing sequences up to dilations in the spirit of Lions [28–31].”
• Some remarks on elliptic problems with critical growth in the gradient (2006, methodology): “In the case λ = λ1(f), using the improved Hardy inequalities (see [51] and [1]), it is possible to prove that problem (13) has a solution v in the space H obtained as the completion of C∞ 0 (Ω) with respect to the norm ||v||(2) = ∫”
• Sharp uncertainty principles on Riemannian manifolds: the influence of curvature (2013, background): “Adimurthi, Chaudhuri and Ramaswamy [1], Barbatis, Filippas and Tertikas [5], Brezis and Vázquez [8], Filippas and Tertikas [20], Ghoussoub and Moradifam [22, 23], Wang and Willem [36], etc.”
• Progress in Mathematics (2013, background): “As a special case we can highlight the case of p = 2 that was also studied by [WW03] in the Euclidean setting.”
• Existence and non-existence of solutions to elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalities (2007, background): “Moreover, some interesting results such as the existence and non-existence of the extremal functions and the symmetry and non-symmetry of the extremal functions were discussed; see [3, 9, 16, 28, 30, 34, 35], for instance.”
• Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities (2004, background): “First we observe that for N−2 2 > a ≥ 0, a ≤ b < a + 1 and a + b 6= 0, when we make a linearization at the radial solution of equation (11), the kernel is generated only by the translation invariance in t of the problem (see [17], [18]).”