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We study the pointwise convergence and the Γ of a family of nonlocal functionals defined in amstex L¹ ₋₎₂ (Rⁿ) to a local functional that depends on the gradient of u and on the set of discontinuity points of u. We apply this result to approximate a minimum problem introduced by Mumford and Shah to study edge detection in computer vision theory. © 1998 John Wiley & Sons, Inc.
Massimo Gobbino (Sun,) studied this question.