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Proceedings of the American Mathematical Society

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

 

 

On solutions of elliptic equations that decay rapidly on paths


Author: D. H. Armitage
Journal: Proc. Amer. Math. Soc. 123 (1995), 2421-2422
MSC: Primary 35J30; Secondary 35B05, 35E20
DOI: https://doi.org/10.1090/S0002-9939-1995-1277091-X
MathSciNet review: 1277091
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Abstract: Let $ P(D)$ be an elliptic differential operator on $ {\mathbb{R}^n}$ with constant coefficients. It is known that if u is a solution of $ P(D)u = 0$ on an unbounded domain and if u decays uniformly and sufficiently rapidly, then $ u = 0$. In this note it is shown that the same conclusion holds if u decays rapidly, but not a priori uniformly, on a sufficiently large set of unbounded paths.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1277091-X
Article copyright: © Copyright 1995 American Mathematical Society