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

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

2010-04-22

arxiv.org/abs/1004.3949v2

Mathematics

Analysis of PDEs

61 pages

Scientific paper

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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