# On the Best Constant for a Weighted Sobolev‐Hardy Inequality

@article{Chou1993OnTB, title={On the Best Constant for a Weighted Sobolev‐Hardy Inequality}, author={Kai-Seng Chou and Chiu Wing Chu}, journal={Journal of The London Mathematical Society-second Series}, year={1993}, volume={48}, pages={137-151} }

## 241 Citations

Electronic Journal of Qualitative Theory of Differential Equations

- Mathematics
- 2016

We show, by way of an example, that numerical bifurcation tools for ODE yield reliable bifurcation diagrams when applied to the pseudospectral approximation of a one-parameter family of nonlinear…

Problemas de minimização com singularidades

- Physics
- 2013

Esta dissertacao trata de resultados de existencia de solucoes de energia minima para as seguintes classes de equacoes elipticas semilineares degeneradas definidas em RN. Consideramos N > 3, os…

Nonradial Solutions to Critical Elliptic Equations of Caffarelli–Kohn–Nirenberg Type

- Mathematics
- 2012

We build an unbounded sequence of nonradial solutions for ∇(|x|−2a∇u)+ |x|− 2N N−2 au N+2 N−2 = 0, u> 0 in RN \{0} , where N ≥ 5 and a< 0. This answers an question of L. Veron.

Asymptotic symmetry and local behaviors of solutions to a class of anisotropic elliptic equations

- Mathematics
- 2011

Let 0 ≤ a 0. Equation (0.1) is arising from the celebrated Caffarelli-Kohn-Nirenberg inequality. For a = b < 0 and p = 2N N−2 , we show there is no positive solution of the equation (0.2) …

On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexistence), and symmetry of extremal functions †

- Mathematics
- 2001

Consider the following inequalities due to Caffarelli, Kohn, and Nirenberg [6]
where, for N ≥ 3, −∞ < a < (N − 2)/2, a ≤ b ≤ a + 1, and p = 2N/(N − 2 + 2(b − a)). We shall answer some…

On critical exponents of a k-Hessian equation in the whole space

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2019

Abstract In this paper, we study negative classical solutions and stable solutions of the following k-Hessian equation $$F_k(D^2V) = (-V)^p\quad {\rm in}\;\; R^n$$with radial structure, where n ⩾ 3,…

Existence of Extremal Functions for Higher-Order Caffarelli–Kohn–Nirenberg Inequalities

- Mathematics
- 2017

Abstract Though there has been an extensive study on first-order Caffarelli–Kohn–Nirenberg inequalities, not much is known for the existence of extremal functions for higher-order ones. The…

Sign-changing solutions for critical equations with Hardy potential

- Mathematics
- 2017

We consider the following perturbed critical Dirichlet problem involving the Hardy-Schrodinger operator on a smooth bounded domain $\Omega \subset \mathbb{R}^N$, $N\geq 3$, with $0 \in \Omega$: $$…