Regularizing estimates for Schrödinger and wave equations
We prove unique continuation for solutions of the inequality , a connected set contained in and is in the Morrey spaces , with and . These spaces include for (see [H], [BKRS]). If , the extra assumption of being small enough is needed.
Let us consider in a domain Ω of Rn solutions of the differential inequality |Δu(x)| ≤ V(x)|u(x)|, x ∈ Ω, where V is a non smooth, positive potential. We are interested in global unique continuation properties. That means that u must be identically zero on Ω if it vanishes on an open subset of Ω.
The purpose of this note is twofold. First it is a corrigenda of our paper [RV1]. And secondly we make some remarks concerning the interpolation properties of Morrey spaces.
Page 1