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Schrödinger operator with magnetic field in domain with corners

Virginie Bonnaillie Noël — 2005

Journées Équations aux dérivées partielles

We present here a simplified version of results obtained with F. Alouges, M. Dauge, B. Helffer and G. Vial (cf [, , ]). We analyze the Schrödinger operator with magnetic field in an infinite sector. This study allows to determine accurate approximation of the low-lying eigenpairs of the Schrödinger operator in domains with corners. We complete this analysis with numerical experiments.

Numerical simulations for nodal domains and spectral minimal partitions

Virginie Bonnaillie-Noël; Bernard Helffer; Gregory Vial — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We recall here some theoretical results of Helffer [ (2007) doi:10.1016/j.anihpc.2007.07.004] about minimal partitions and propose numerical computations to check some of their published or unpublished conjectures and exhibit new ones.

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