Strong uniqueness for Schrödinger operators with Kato potentials
The author proves a strong unique continuation result for Schrödinger inequalities with radial Kato potential, i.e. if \(u \in H^1_{\text{loc}} (B(x_0, R_0))\), \(|\Delta u |\leq |Vu |\), where \(V\) is a radial potential such that \[ \lim_{r \to 0} \sup_{x \in B (x_0, R_0)} \int_{|x - y |< r} {\bigl |V(y) \bigr |\over |x - y |^{d - 2}} dy = 0 \;\text{and} \int_{|x - x_0 |< r} |u |^2 dx = O(r^N), \;r \to 0, \;\forall N > 0, \] then \(u\) should be zero.
scientific article; zbMATH DE number 850622