Search results for "Hardy"

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.

Large Hardy-Weinberg equilibrium deviations in the Daphnia longispina of Lake El Tobar

1995

The population structure of Daphnia longispina in Lake El Tobar, Spain was studied by measuring variation at the aldehyde oxidase (AO), phosphoglucose isomerase (PGI) and phosphoglucose mutase (PGM) loci in each of 1337 individuals from four collections. In 9 of the 12 comparisons between observed allele frequencies and those expected by Hardy-Weinberg equilibrium there was an excess of heterozygotes. We found 27 of the potential number of 54 composite electromorphs (‘clones’) based on the three allozymes. Clone diversities were rather high in all collections. Three clones reached frequencies of over 25% and different clones were dominant in each of the four collections. Strong temporal var…

Some remarks on nonlinear elliptic problems involving Hardy potentials

2007

In this note we prove an Hardy type inequality with a remainder term, where the potential depends only on a group of variables. Such a result allows us to show the existence of entropy solutions to a class of elliptic P.D.E.'s.

The figurative path to Thomas Hardy's Far from the madding crowd

2001

Konstruktivistinen naiskuva ja sen rakentuminen Thomas Hardyn romaanissa Tess of the d'Urbervilles

2006

Weighted Hardy inequalities and the boundary size

2008

Assouad Type Dimensions in Geometric Analysis

2021

We consider applications of the dual pair of the (upper) Assouad dimension and the lower (Assouad) dimension in analysis. We relate these notions to other dimensional conditions such as a Hausdorff content density condition and an integrability condition for the distance function. The latter condition leads to a characterization of the Muckenhoupt Ap properties of distance functions in terms of the (upper) Assouad dimension. It is also possible to give natural formulations for the validity of Hardy–Sobolev inequalities using these dual Assouad dimensions, and this helps to understand the previously observed dual nature of certain cases of these inequalities. peerReviewed

Weighted Hardy Spaces of Quasiconformal Mappings

2019

We establish a weighted version of the $H^p$-theory of quasiconformal mappings.

Rectifiability and singular integrals

1995

A Perturbed Cauchy Viscoelastic Problem in an Exterior Domain

2023

A Cauchy viscoelastic problem perturbed by an inverse-square potential, and posed in an exterior domain of RN, is considered under a Dirichlet boundary condition. Using nonlinear capacity estimates specifically adapted to the non-local nature of the problem, the potential function and the boundary condition, we establish sufficient conditions for the nonexistence of weak solutions.