On some properties of solutions of Helmholtz equation
Alexander G. Ramm · Journal of Mathematical Physics · 1981
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.