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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Equivalence of the Green's functions for diffusion operators in $ {\bf R}\sp{n}$: a counterexample


Author: Patricia Bauman
Journal: Proc. Amer. Math. Soc. 91 (1984), 64-68
MSC: Primary 35J15
DOI: https://doi.org/10.1090/S0002-9939-1984-0735565-4
MathSciNet review: 735565
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Abstract: In a smooth domain in $ {{\mathbf{R}}^n}$, the Green's functions for second-order, uniformly elliptic operators in divergence form are all proportional to the Green's function for the Laplacian [7]. In this paper we show that the above result fails for diffusion operators, that is, second-order, uniformly elliptic operators with continuous coefficients in nondivergence form. In fact, we give an example in which the Green's function is locally unbounded away from the pole.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0735565-4
Article copyright: © Copyright 1984 American Mathematical Society