On the behavior at collisions of solutions to Schr "odinger equations\n with many-particle and cylindrical potentials

2010/04/22 by Veronica Felli, Felli, Veronica, Alberto Ferrero +3 · 1 citation
Mathematics · #35B40 #35J10 #35J60 #81V70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1004.3949

openalex publication_date 2010/04/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

The asymptotic behavior of solutions to Schr "odinger equations with singular\nhomogeneous potentials is investigated. Through an Almgren type monotonicity\nformula and separation of variables, we describe the exact asymptotics near the\nsingularity of solutions to at most critical semilinear elliptic equations with\ncylindrical and quantum multi-body singular potentials. Furthermore, by an\niterative Brezis-Kato procedure, point-wise upper estimate are derived.\n

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