Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

Veronica Felli; Alberto Ferrero; Susanna Terracini

doi:10.4171/JEMS/246

Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

Veronica Felli, Alberto Ferrero, Susanna Terracini

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

Abstract

Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using an Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with homogeneity of order-1.

Lingua originale	Inglese
pagine (da-a)	119-174
Numero di pagine	56
Rivista	Journal of the European Mathematical Society
Volume	13
Numero di pubblicazione	1
DOI	https://doi.org/10.4171/JEMS/246
Stato di pubblicazione	Pubblicato - 2011
Pubblicato esternamente	Sì

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10.4171/JEMS/246

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title = "Asymptotic behavior of solutions to Schr{\"o}dinger equations near an isolated singularity of the electromagnetic potential",

abstract = "Asymptotics of solutions to Schr{\"o}dinger equations with singular magnetic and electric potentials is investigated. By using an Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with homogeneity of order-1.",

keywords = "Hardy's inequality, Schr{\"o}dinger operators, Singular electromagnetic potentials",

author = "Veronica Felli and Alberto Ferrero and Susanna Terracini",

year = "2011",

doi = "10.4171/JEMS/246",

language = "English",

volume = "13",

pages = "119--174",

journal = "Journal of the European Mathematical Society",

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T1 - Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

AU - Felli, Veronica

AU - Ferrero, Alberto

AU - Terracini, Susanna

PY - 2011

Y1 - 2011

N2 - Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using an Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with homogeneity of order-1.

AB - Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using an Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with homogeneity of order-1.

KW - Hardy's inequality

KW - Schrödinger operators

KW - Singular electromagnetic potentials

U2 - 10.4171/JEMS/246

DO - 10.4171/JEMS/246

M3 - Article

SN - 1435-9855

VL - 13

SP - 119

EP - 174

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 1

ER -

Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

Abstract

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