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

Veronica Felli | Zendy; Alberto Ferrero | Zendy; Susanna Terracini | Zendy

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

Author(s) -

Veronica Felli,

Alberto Ferrero,

Susanna Terracini

Publication year - 2012

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2012.32.3895

Subject(s) - pointwise , singularity , monotonic function , schrödinger equation , mathematical analysis , type (biology) , quantum , homogeneous , mathematical physics , mathematics , physics , quantum mechanics , statistical physics , ecology , biology

The asymptotic behavior of solutions to Schr\"odinger 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, point-wise upper estimate are derived.

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