On semilinear elliptic equations with borderline Hardy potentials

Veronica Felli; Alberto Ferrero

doi:10.1007/s11854-014-0022-9

On semilinear elliptic equations with borderline Hardy potentials

Veronica Felli
, Alberto Ferrero

Department of Science and Technological Innovation

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	303-340
Number of pages	38
Journal	Journal d'Analyse Mathematique
Volume	123
Issue number	1
DOIs	https://doi.org/10.1007/s11854-014-0022-9
Publication status	Published - Jul 2014

Access to Document

10.1007/s11854-014-0022-9

Cite this

@article{c26b1293ddfc449ca581086efc388f86,

title = "On semilinear elliptic equations with borderline Hardy potentials",

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.",

author = "Veronica Felli and Alberto Ferrero",

year = "2014",

month = jul,

doi = "10.1007/s11854-014-0022-9",

language = "English",

volume = "123",

pages = "303--340",

journal = "Journal d'Analyse Mathematique",

issn = "0021-7670",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - On semilinear elliptic equations with borderline Hardy potentials

AU - Felli, Veronica

AU - Ferrero, Alberto

PY - 2014/7

Y1 - 2014/7

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84904904017

U2 - 10.1007/s11854-014-0022-9

DO - 10.1007/s11854-014-0022-9

M3 - Article

SN - 0021-7670

VL - 123

SP - 303

EP - 340

JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

IS - 1

ER -

On semilinear elliptic equations with borderline Hardy potentials

Abstract

Access to Document

Other files and links

Fingerprint

Cite this