Ground state for the Schrödinger operater with the weighted Hardy potential

Details Ground state for the Schrödinger operater with the weighted Hardy potential Ground state for the Schrödinger operater with the weighted Hardy potential

2011-04-12

arxiv.org/abs/1104.2160v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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