Density theorems for local minimizers of area-type functionals

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1. [1] W.K. Allard - F.J. Almgren, Geometric measure theory and the calculus of variations, Proceed. Symposia Pure Math., Vol. 44, American Math. Society, Providence (1986). Zbl0577.00014MR840266
2. [2] F.J. Almgrenjr., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraint, Mem. Amer. Math. Soc., 4, n. 165 (1976). Zbl0327.49043MR420406
3. [3] L. Ambrosio, A compactness theorem for a special class of functions of bounded variation, Boll. U.M.I., 3-B (1989), pp. 857-888. Zbl0767.49001MR1032614
4. [4] L. Ambrosio, Existence theory for a new class of variational problems, Arch. Rational Mech. Anal., 111, (1990), pp. 291-322 Zbl0711.49064MR1068374
5. [5] L. Ambrosio - S. Mortola - V.M. Tortorelli, Funzioni a variazione limitata generalizzate, to appear. 
6. [6] E. Barozzi - I. Tamanini, Penalty methods for minimal surfaces with obstacles, Ann. Mat. Pura Appl., 152 (1988), pp. 139-157. Zbl0824.49035MR980976
7. [7] M. Carriero - A. Leaci - D. Pallara - E. Pascali, Euler conditions for a minimum problem with free discontinuity surfaces, preprint Dip. Mat. Univ.Lecce (1988). 
8. [8] G. Concedo - I. Tamanini, Note sulla regotarita dei minimi di funzionati del tipo dell'area, Rend. Acc. Naz. Sci. XL, Mem. Mat., 12 (1988), pp. 238-257. 
9. [9] E. DeGIORGI, Su una teoria generale della misura (r - 1)-dimensionale in uno spazio ad r dimensioni, Ann. Mat. Pura Appl., 36 (1954), pp. 191-213. Zbl0055.28504MR62214
10. [10] E. De Giorgi, Nuovi teoremi relativi alle misure (r -1)-dimensionali in uno spazio ad r dimensioni, Ricerche di Matematica, 4 (1955), pp. 95-113. Zbl0066.29903MR74499
11. [11] E. De Giorgi, Sulla proprietà isoperimetrica dell'ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita, Atti Accad. Naz. Lincei (Serie VIII), 5 (1958), pp. 33-44. Zbl0116.07901MR98331
12. [12] E. DeGIORGI - I. AMBROSIO, Un nuovo tipo di funzionale del calcolo delle variazioni, AttiAccad. Naz. Lincei (8), 82 (1988), pp. 199-210. Zbl0715.49014MR1152641
13. [13] E. DeGIORGI - M. CARRIERO - A. LEACI, Existence theoremfor a minimum problem withfree discontinuity set, Arch. Rational Mech. Anal., 108 (1989), pp. 195-218. Zbl0682.49002MR1012174
14. [14] E. De Giorgi - F. Colombini - I. Piccinini, Frontiere orientate di misura minima e questioni collegate, Editrice Tecnico Scientifica, Pisa (1972). Zbl0296.49031MR179651
15. [15] E. DeGIORGI - G. CONGEDO - I. TAMANINI, Problemi di regolarità per un nuovo tipo di funzionale del calcolo delle variazioni, AttiAccad. Naz. Lincei (8), 82 (1988), pp. 673-678. Zbl0735.49036MR1139814
16. [16] H. Federer, Geometric Measure Theory, Springer-Verlag, Berlin-Heidelberg-New York (1969). Zbl0176.00801MR257325
17. [17] E. Giusti, Minimal surfaces and functions of bounded variation, Boston -Basel-Stuttgart (1984). Zbl0545.49018MR775682
18. [18] U. Massari, Insiemi di perimetro finito su varietà, Boll. U.M.I. (6), 3-B (1984), pp. 149-169. Zbl0556.49023
19. [19] U. Massari - M. Miranda, Minimal Surfaces of Codimension One, North-Holland, Amsterdam (1984). Zbl0565.49030MR795963
20. [20] V.G. Maz'ja, Sobolev Spaces, Springer-Verlag (1985). MR817985
21. [21] J.M. Morel - S. Solimini, Segmentation of images by variational methods: a constructive approach, Rev. Mat. Univ. Complutense Madrid, 1 (1988), pp. 169-182. Zbl0679.68205MR977048
22. [22] D. Mumford - J., Shah, Boundary detection by minimizing functionals, preprint. 
23. [23] D. Mumford - J. SHAH, Optimal approximations by piecewice smooth functions and associated variational problems, Comm. Pure Appl. Math., 42 (1989), pp. 577-685. Zbl0691.49036MR997568
24. [24] I. Tamanini, Regularity results for almost minimal oriented hypersurfaces in Rn, Quaderni Dip. Mat. Univ. Lecce, n. 1 (1984). Zbl1191.35007
25. [25] J.E. Taylor, The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces, Ann. Math., 103 (1976), pp. 489-539. Zbl0335.49032MR428181
26. [26] J.E. Taylor, Crystalline variational problems, Bull. A.M.S., 84 (1978), pp. 568-588. Zbl0392.49022MR493671
27. [27] E. Virga, Sulle forme di equilibrio di una goccia di cristallo liquido, Atti Sem. Mat. Fis. Univ. Modena, 38 (1990), pp. 29-38. Zbl0698.76109
28. [28] A.I. Volpert, Spaces BV and quasi-linear equations, Math. USSR Sbornik, 17 (1967), pp. 225-267. 
29. [29] L. Ambrosio - A. Braides, Functionals defined on partitions ... - I e II, J. Math. Pures Appl., 69 (1990), pp. 285-305 e pp. 307-333. Zbl0676.49029
30. [30] G. Congedo - I. Tamanini, On the existence of solutions to a problem in multidimensional segmentation, Ann. Inst. H. Poincaré, Anal. non Linéaire, 8 (1991), pp. 175-195. Zbl0729.49003MR1096603
31. [31] U. Massari - I. Tamanini, Regularity properties of optimal segmentations, J. Reine Angew. Math. (1991), to appear. Zbl0729.49004MR1124566

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