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On the equivalence of Green functions for general Schrödinger operators on a half-space
2004
Annales Polonici Mathematici
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We consider the general Schrödinger operator L = div(A(x)∇ x ) − µ on a half-space in R n , n ≥ 3. We prove that the L-Green function G exists and is comparable to the Laplace-Green function G ∆ provided that µ is in some class of signed Radon measures. The result extends the one proved on the half-plane in [9] and covers the case of Schrödinger operators with potentials in the Kato class at infinity K ∞ n considered by Zhao and Pinchover. As an application we study the cone C L (R n + ) of all
doi:10.4064/ap83-1-8
fatcat:dxwhpm5ppbdvjhzete4r67oyiu