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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
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.

References [Enhancements On Off] (What's this?)

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