In this paper, we study the asymptotic behavior of solutions of 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.
On semilinear elliptic equations with borderline Hardy potentials
FERRERO, ALBERTO
2014-01-01
Abstract
In this paper, we study the asymptotic behavior of solutions of 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.File in questo prodotto:
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