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• W2084594767 startingPage "54" @default.
• W2084594767 abstract "Let P be a second order elliptic operator which is defined on a domain Ω ⊆ R n and let W ( x ) be a nonzero nonnegative function. Assume that P λ = P − λW ( x ) admits a positive minimal Green function G Pλ Ω (x, y) for all λ< 0. We prove that lim λ→0 λ<0 (−λ) G P λ Ω (x,y) = F(x,y) where F = 0 for x ≠ y , unless P and P ∗ admit ground states φ ( x ) and ϑ ( x ), respectively, with eigenvalue zero such that ∫ Ω φ(z) W(z) ϑ(z) dz < ∞ . In this case F(x,y)= φ(x)ϑ(y) ∫ Ω φ(z) W(z) ϑ(z) dx Moreover, if ∫ Ω φ(z) ϑ(z) dz < ∞ , then the heat kernel k ( x , y , t ) of the parabolic equation Lu ≡ u t + Pu = 0 satisfies lim t→∞ k(x,y,t)= φ(x)ϑ(y) ∫ Ω φ(z) ϑ(z) dz" @default.
• W2084594767 created "2016-06-24" @default.
• W2084594767 creator A5016714048 @default.
• W2084594767 date "1992-02-01" @default.
• W2084594767 modified "2023-09-27" @default.
• W2084594767 title "Large time behavior of the heat kernel and the behavior of the Green function near criticality for nonsymmetric elliptic operators" @default.
• W2084594767 cites W1548014566 @default.
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• W2084594767 doi "https://doi.org/10.1016/0022-1236(92)90090-6" @default.
• W2084594767 hasPublicationYear "1992" @default.
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