Abstract
We consider on a bounded domain \(\Omega \subset {\mathbb{R}}^N\) , the Schrödinger operator − Δ − V supplemented with Dirichlet boundary solutions. The potential V is either the critical inverse square potential V(x) = (N − 2)2/4|x|−2 or the critical borderline potential V(x) = (1/4)dist(x, ∂Ω)−2. We present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator in each case, based on recent results on improved Hardy–Sobolev type inequalities.
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Karachalios, N.I. Weyl’s Type Estimates on the Eigenvalues of Critical Schrödinger Operators. Lett Math Phys 83, 189–199 (2008). https://doi.org/10.1007/s11005-007-0218-3
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DOI: https://doi.org/10.1007/s11005-007-0218-3