Search results for "Hardy's inequality"
showing 6 items of 6 documents
Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential
2016
Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations
Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential
2016
Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations −Δpu − μ |x| p |u| p−2 u + m|u| p−2 u = f(u), x ∈ RN , where 1 0 and f is a continuous function. peerReviewed
Hardy’s inequality and the boundary size
2002
We establish a self-improving property of the Hardy inequality and an estimate on the size of the boundary of a domain supporting a Hardy inequality.
Asymptotic Behaviors of Solutions to quasilinear elliptic Equations with critical Sobolev growth and Hardy potential
2015
Abstract Optimal estimates on the asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations − Δ p u − μ | x | p | u | p − 2 u = Q ( x ) | u | N p N − p − 2 u , x ∈ R N , where 1 p N , 0 ≤ μ ( ( N − p ) / p ) p and Q ∈ L ∞ ( R N ) .
Quasiadditivity of Variational Capacity
2013
We study the quasiadditivity property (a version of superadditivity with a multiplicative constant) of variational capacity in metric spaces with respect to Whitney type covers. We characterize this property in terms of a Mazya type capacity condition, and also explore the close relation between quasiadditivity and Hardy's inequality.
Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential
2015
This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\, x\in\mathbb{R}^{N}, \] where $1<p<N,0\leq\mu<\left((N-p)/p\right)^{p}$ and $Q\in L^{\infty}(\R^{N})$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.