On semilinear elliptic equations with borderline Hardy potentials
Analysis of PDEs
2012-09-24 v1
Abstract
In this paper we study the asymptotic behavior of solutions to an elliptic equation near the singularity of an inverse square potential with a coefficient related to the best constant for the Hardy inequality. Due to the presence of a borderline Hardy potential, a proper variational setting has to be introduced in order to provide a weak formulation of the equation. An Almgren-type monotonicity formula is used to determine the exact asymptotic behavior of solutions.
Cite
@article{arxiv.1209.4852,
title = {On semilinear elliptic equations with borderline Hardy potentials},
author = {Veronica Felli and Alberto Ferrero},
journal= {arXiv preprint arXiv:1209.4852},
year = {2012}
}