Ill-Posedness of sublinear minimization problems
Murugesan, C. (2011). Ill-Posedness of sublinear minimization problems. EKB Journal Management System, 19(1), 88-90. doi: 10.1016/j.joems.2011.09.004
C. Murugesan. "Ill-Posedness of sublinear minimization problems". EKB Journal Management System, 19, 1, 2011, 88-90. doi: 10.1016/j.joems.2011.09.004
Murugesan, C. (2011). 'Ill-Posedness of sublinear minimization problems', EKB Journal Management System, 19(1), pp. 88-90. doi: 10.1016/j.joems.2011.09.004
Murugesan, C. Ill-Posedness of sublinear minimization problems. EKB Journal Management System, 2011; 19(1): 88-90. doi: 10.1016/j.joems.2011.09.004

Ill-Posedness of sublinear minimization problems

Journal of the Egyptian Mathematical Society
Volume 19, Issue 1, June 2011, Pages 88-90    PDF (336.75 K)
DOI: 10.1016/j.joems.2011.09.004
Author
C. Murugesan
Department of Mathematics, SATHYABAMA University, Chennai 600 119, India
Abstract
It is well known that minimization problems involving sublinear regularization terms are ill-posed, in Sobolev spaces. Extended results to spaces of bounded variation functions BV were recently showed in the special case of bounded regularization terms. In this note, a generalization to sublinear regularization is presented in BV spaces. Notice that our results are optimal in the sense that linear regularization leads to well-posed minimization problems in BV spaces.
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