Schecter, M. and Simon, B. (1980) Unique continuation for Schrodinger operators with unbounded potentials. Journal of Mathematical Analysis and Applictions, 77 (2). pp. 482-492. ISSN 0022-247X. doi:10.1016/0022-247X(80)90242-5. https://resolver.caltech.edu/CaltechAUTHORS:20180521-164135228
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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^∞.
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| 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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| Issue or Number: | 2 | ||||||
| DOI: | 10.1016/0022-247X(80)90242-5 | ||||||
| Record Number: | CaltechAUTHORS:20180521-164135228 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180521-164135228 | ||||||
| Official Citation: | M Schechter, B Simon, Unique continuation for Schrodinger operators with unbounded potentials, Journal of Mathematical Analysis and Applications, Volume 77, Issue 2, 1980, Pages 482-492, ISSN 0022-247X, https://doi.org/10.1016/0022-247X(80)90242-5. (http://www.sciencedirect.com/science/article/pii/0022247X80902425) | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 86535 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | George Porter | ||||||
| Deposited On: | 22 May 2018 16:06 | ||||||
| Last Modified: | 15 Nov 2021 20:39 |
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