A pr 2 00 4 Estimates on the Lower Bound of the First Gap ∗
نویسنده
چکیده
We give a lower bound for the first gap λ2 − λ1 of the Dirichlet eigenvalues of the Schrödinger operator on a bounded convex domain Ω in a class of Riemannian manifolds, namely λ2 − λ1 ≥ π diameter(Ω) + ( 12 π − 1)α. For the Laplacian on disks in Rn, we have λ2 − λ1 ≥ 4 3 π diameter(Ω) .
منابع مشابه
J an 2 00 5 Estimates on the Lower Bound of the First Gap ∗
We give a new lower bound for the first gap λ2−λ1 of the Dirichlet eigenvalues of the Schrödinger operator on a bounded convex domain Ω in Rn or Sn and greatly sharpens the previous estimates. The new bound is explicit and computable.
متن کامل1 M ay 2 00 4 Estimates on the Lower Bound of the First Gap ∗
We give a lower bound for the first gap λ2 − λ1 of the Dirichlet eigenvalues of the Schrödinger operator on a bounded convex domain Ω in a class of Riemannian manifolds, namely λ2 − λ1 ≥ π diameter(Ω) + ( 12 π − 1)α. For the Laplacian on disks in Rn, we have λ2 − λ1 ≥ 4 3 π diameter(Ω) .
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تاریخ انتشار 1997