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.
Felli, V., Ferrero, A., Terracini, S. (2012). On the behavior at collisions of solutions to Schrödinger equations with many-particle and cylindrical potentials. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 32(11), 3895-3956 [10.3934/dcds.2012.32.3895].
On the behavior at collisions of solutions to Schrödinger equations with many-particle and cylindrical potentials
FELLI, VERONICA;TERRACINI, SUSANNA
2012
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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preprint_quantum_N_body.pdf
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