On the behavior at collisions of solutions to schrödinger equations with many-particle and cylindrical potentials

Veronica Felli; Alberto Ferrero; Susanna Terracini

doi:10.3934/dcds.2012.32.3895

On the behavior at collisions of solutions to schrödinger equations with many-particle and cylindrical potentials

Veronica Felli
, Alberto Ferrero
, Susanna Terracini

Dipartimento di Scienze e Innovazione Tecnologica

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

Abstract

The asymptotic behavior of solutions to Schrödinger equations with singular homogeneous potentials is investigated. Through an Almgren type monotonicity formula and separation of variables, we describe the exact asymptotics near the singularity of solutions to at most critical semilinear elliptic equations with cylindrical and quantum multi-body singular potentials. Furthermore, by an iterative Brezis-Kato procedure, pointwise upper estimate are derived.

Lingua originale	Inglese
pagine (da-a)	3895-3956
Numero di pagine	62
Rivista	Discrete and Continuous Dynamical Systems
Volume	32
Numero di pubblicazione	11
DOI	https://doi.org/10.3934/dcds.2012.32.3895
Stato di pubblicazione	Pubblicato - nov 2012

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10.3934/dcds.2012.32.3895

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title = "On the behavior at collisions of solutions to schr{\"o}dinger equations with many-particle and cylindrical potentials",

abstract = "The asymptotic behavior of solutions to Schr{\"o}dinger equations with singular homogeneous potentials is investigated. Through an Almgren type monotonicity formula and separation of variables, we describe the exact asymptotics near the singularity of solutions to at most critical semilinear elliptic equations with cylindrical and quantum multi-body singular potentials. Furthermore, by an iterative Brezis-Kato procedure, pointwise upper estimate are derived.",

keywords = "Hardy's inequality, Quantum N-body problem, Schr{\"o}dinger operators, Singular cylindrical potentials",

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

year = "2012",

month = nov,

doi = "10.3934/dcds.2012.32.3895",

language = "English",

volume = "32",

pages = "3895--3956",

journal = "Discrete and Continuous Dynamical Systems",

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AU - Felli, Veronica

AU - Ferrero, Alberto

AU - Terracini, Susanna

PY - 2012/11

Y1 - 2012/11

N2 - The asymptotic behavior of solutions to Schrödinger equations with singular homogeneous potentials is investigated. Through an Almgren type monotonicity formula and separation of variables, we describe the exact asymptotics near the singularity of solutions to at most critical semilinear elliptic equations with cylindrical and quantum multi-body singular potentials. Furthermore, by an iterative Brezis-Kato procedure, pointwise upper estimate are derived.

AB - The asymptotic behavior of solutions to Schrödinger equations with singular homogeneous potentials is investigated. Through an Almgren type monotonicity formula and separation of variables, we describe the exact asymptotics near the singularity of solutions to at most critical semilinear elliptic equations with cylindrical and quantum multi-body singular potentials. Furthermore, by an iterative Brezis-Kato procedure, pointwise upper estimate are derived.

KW - Hardy's inequality

KW - Quantum N-body problem

KW - Schrödinger operators

KW - Singular cylindrical potentials

UR - https://www.scopus.com/pages/publications/84867025828

U2 - 10.3934/dcds.2012.32.3895

DO - 10.3934/dcds.2012.32.3895

M3 - Article

SN - 1078-0947

VL - 32

SP - 3895

EP - 3956

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 11

ER -

On the behavior at collisions of solutions to schrödinger equations with many-particle and cylindrical potentials

Abstract

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