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7550159 
Journal Article 
Existence of Minimizers for a Class of Anisotropic Free Discontinuity Problems 
Trombetti, C 
1999 
Yes 
Annali di Matematica Pura ed Applicata
ISSN: 0373-3114
EISSN: 1618-1891 
SPRINGER HEIDELBERG 
HEIDELBERG 
177 
1 
277-292 
WOS:000208513500010 
We prove the existence of minimizing pairs (K, u), K compact set of R-N and u is an element of W-1,W- (p) (Omega\K), for the functional G(K, u) = integral(Omega\K) f(x, del u) + alpha integral(Omega\K) vertical bar u - g vertical bar(q) + beta HN - 1(K boolean AND Omega) when the integrand f(x, z) is convex with respect to z, vertical bar z vertical bar(p) <= f(x, z) <= L vertical bar z vertical bar(p), p > 1, and satisfies suitable assumptions of uniform continuity in x with respect to z.