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

Veronica Felli; Alberto Ferrero; Susanna Terracini

doi:10.3934/dcds.2012.32.3895

Article Contents

2012, Volume 32, Issue 11: 3895-3956. Doi: 10.3934/dcds.2012.32.3895

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

1.
Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano
2.
Università degli Studi del Piemonte Orientale, Viale Teresa Michel 11, 15121 Alessandria

Received: June 30, 2011

Revised: November 30, 2011

Published: October 2012

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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.

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Mathematics Subject Classification: Primary: 35J10, 35B40, 35J60; Secondary: 81V70.

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