TY - JOUR
T1 - On the behavior at collisions of solutions to schrödinger equations with many-particle and cylindrical potentials
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 -