Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

Abstract

Asymptotics of solutions to Schroedinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order -1.

References in corpus (1)

• On Schrödinger operators with multisingular inverse-square anisotropic potentials

Cited by in corpus (2)

• Singularity of eigenfunctions at the junction of shrinking tubes, Part II
• Nodal sets of magnetic Schroedinger operators of Aharonov-Bohm type and energy minimizing partitions