Unique continuation for Schrodinger operators with unbounded potentials

Creators: Schecter, M.; Simon, B.

Abstract

We consider unique continuation theorems for solution of inequalities ¦Δu(x)¦ ⩽ W(x) ¦u(x)¦ with W allowed to be unbounded. We obtain two kinds of results. One allows W ϵ L^p_(loc)(R^n) with p ⩾ n − 2forn > 5, p >13(2n − 1)forn ⩽ 5. The other requires fW^2 to be −Δ-form bounded for all f ϵ C_0^∞.

Additional Information

© 1980 Published by Elsevier. Submitted by C. L. Dolph. Research partially supported by U.S. National Science Foundation under Grants MCS-76-04833 (Schechter) and MCS-78-01885 (Simon). We would like to thank Lavine for raising this problem and one of us (B.S.) would like to thank Yeshiva University for its hospitality in 1976-77 when he was a visitor and this research was initiated. We would like to thank W. Amrein, A. M. Berthier and V. Georesgu for pointing out an error in a preliminary version of this paper.

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Unique continuation for Schrodinger operators with unbounded potentials

Abstract

Additional Information

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