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A note on solutions of the Schrödinger equation. (English) Zbl 0770.31008

(Author’s abstract.) Using a suitable geometric series a simple proof for the continuity of \(L^ 1\)-solutions of the Schrödinger equation \(Lu:=\Delta u-Vu\) \((V\) being a Kato function) is obtained. It works as well for uniformly elliptic operators having Hölder continuous coefficients and Kato measures instead of Kato functions. Moreover, it is shown that results on singularities are immediate consequences of the local existence of continuous Green functions for \(L\).
Reviewer: M.Dont (Praha)

MSC:

31D05 Axiomatic potential theory
35J10 Schrödinger operator, Schrödinger equation
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