We study some properties of a nonconvex variational problem. The infimum of the functional that has to be minimized fails to be attained. Instead, minimizing sequences develop gradient oscillations which allow them to decrease the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original non perturbed problem is analyzed numerically.
Analysis of a nonconvex problem related to signal selective smoothing
March R;
1997
Abstract
We study some properties of a nonconvex variational problem. The infimum of the functional that has to be minimized fails to be attained. Instead, minimizing sequences develop gradient oscillations which allow them to decrease the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original non perturbed problem is analyzed numerically.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
