Equivalence of the Green’s functions for diffusion operators in $\textbf {R}^{n}$: a counterexample
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- by Patricia Bauman PDF
- Proc. Amer. Math. Soc. 91 (1984), 64-68 Request permission
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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- 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