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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 930978, 8 pages
Research Article

There Are Thin Minimizers of the L1TV Functional

Department of Mathematics, Washington State University, Pullman, WA 99164-3113, USA

Received 18 June 2012; Accepted 30 July 2012

Academic Editor: Ondřej Došlý

Copyright © 2012 Benjamin Van Dyke and Kevin R. Vixie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We show the surprising results that while the local reach of the boundary of an 𝐿 1 𝑇 𝑉 minimizer is bounded below by 1 / 𝜆 , the global reach can be smaller. We do this by demonstrating several example minimizing sets not equal to the union of the 1 / 𝜆 -balls they contain.