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## Ground state for the Schr\"odinger operater with the weighted Hardy potential

### Abstract

We establish the existence of ground states on Euclidean space for the Laplace operator involving the Hardy type potential. This gives rise to the existence of the principal eigenfunctions for the Laplace operator involving weighted Hardy potentials. We also obtain a higher integrability property for the principal eigenfunction. This is used to examine the behaviour of the principal eigenfunction around 0

Topics: Mathematics - Analysis of PDEs, 35J 35, 35J.50, 35J67
Year: 2011
OAI identifier: oai:arXiv.org:1104.2160