On some properties of solutions of Helmholtz equation
- 1 February 1981
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 22 (2) , 275-276
- https://doi.org/10.1063/1.524900
Abstract
We give a new method to prove results of the following type. Let: (∇2 + k2)u=0 in DR={x‖x‖?R}, k2≳0. (1) If u∈L2(DR), then u≡0 in DR. (2) If ‖x‖mu(x)→0 as ‖x‖→∞, x21+⋅⋅⋅+x2N−1?cx−2pN ,p≳0, m=1, 2, 3,..., ‖x‖[(∂u/∂‖x‖)−iku‖x‖→∞]→0, then u≡0 in DR.Keywords
This publication has 2 references indexed in Scilit:
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- Growth properties of solutions of the reduced wave equation with a variable coefficientCommunications on Pure and Applied Mathematics, 1959