Estimates for Green’s functions
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- by A. G. Ramm and Lige Li
- Proc. Amer. Math. Soc. 103 (1988), 875-881
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947673-7
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Abstract:
Let ${l_q} = - {\nabla ^2} + q(x),x \in {R^3},0 \leq q \leq c{(1 + \left | x \right |)^{ - a}},a{\text { > }}2,{l_q}{G_q}(x,y) = \delta (x - y)$. If $q \geq p \geq 0,q \not \equiv p$, then $\begin {gathered} c\left | {x - y\left | {^{ - 1}} \right .{\text { < }}{{\text {G}}_q}(x,y){\text { < }}} \right .{G_p}(x,y) \leq {(4\pi \left | {x - y} \right |)^{ - 1}},x \ne y \end {gathered}$, for some positive $c = c(q)$. If $p \not \equiv 0$ then ${G_p}{\text { < }}{(4\pi \left | {x - y} \right |)^{ - 1}},x \ne y$.References
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Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 875-881
- MSC: Primary 35J15; Secondary 35A08
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947673-7
- MathSciNet review: 947673