We will present the results obtained in collaboration with Alberto Ferrero and Susanna Terracini about the asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials. 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.
Felli, V. (2009). Monotonicity methods for asymptotics of solutions to Schrödinger equations near isolated singularities of the electromagnetic potential. Intervento presentato a: Lack of Compactness in Nonlinear Problems: Prospects and Applications, CIRM, Luminy.
Monotonicity methods for asymptotics of solutions to Schrödinger equations near isolated singularities of the electromagnetic potential
FELLI, VERONICA
2009
Abstract
We will present the results obtained in collaboration with Alberto Ferrero and Susanna Terracini about the asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials. 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.
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