Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896746 | Journal of Functional Analysis | 2018 | 39 Pages |
Abstract
We consider the Schrödinger operator âÎ+V for negative potentials V, on open sets with positive first eigenvalue of the Dirichlet-Laplacian. We show that the spectrum of âÎ+V is positive, provided that V is greater than a negative multiple of the logarithmic gradient of the solution to the Lane-Emden equation âÎu=uqâ1 (for some 1â¤q<2). In this case, the ground state energy of âÎ+V is greater than the first eigenvalue of the Dirichlet-Laplacian, up to an explicit multiplicative factor. This is achieved by means of suitable Hardy-type inequalities, that we prove in this paper.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Lorenzo Brasco, Giovanni Franzina, Berardo Ruffini,