Geodesic
Regularity of Minimizers for a Class of Anistropic Free Discontinuity Problems
Journal of convex analysis, Tome 8 (2001) no. 2, pp. 349-368 Cet article a éte moissonné depuis la source Heldermann Verlag

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This paper contains existence and regularity results for solutions u from Ω to (Rn)N of a class of free discontinuity problems i. e.: the energy to minimize consists of both a bulk and a surface part. The main feature of the class of problems considered here is that the energy density of the bulk part is supposed to be fully anisotropic with p-growth in the scalar case, n = 1. Similar results for the vectorial case n >1 are obtained for radial energy densities, being anisotropic again with p growth. 
@article{JCA_2001_8_2_JCA_2001_8_2_a2,
     author = {N. Fusco and G. Mingione and C. Trombetti},
     title = {Regularity of {Minimizers} for a {Class} of {Anistropic} {Free} {Discontinuity} {Problems}},
     journal = {Journal of convex analysis},
     pages = {349--368},
     year = {2001},
     volume = {8},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a2/}
}
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N. Fusco; G. Mingione; C. Trombetti. Regularity of Minimizers for a Class of Anistropic Free Discontinuity Problems. Journal of convex analysis, Tome 8 (2001) no. 2, pp. 349-368. http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a2/