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Unique continuation for Schrodinger operators with unbounded potentials

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^∞.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0022-247X(80)90242-5DOIArticle
ORCID:
AuthorORCID
Simon, B.0000-0003-2561-8539
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.
Funders:
Funding AgencyGrant Number
NSFMCS-76-04833
NSFMCS-78-01885
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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