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Regularity of minimal boundaries with obstacles. (English) Zbl 0494.49030


MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
49J40 Variational inequalities
35R35 Free boundary problems for PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
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References:

[1] M. Miranda , Frontiere minimali con ostacoli , Ann. Univ. Ferrara , 16 ( 1971 ), pp. 29 - 37 . MR 301617 | Zbl 0266.49036 · Zbl 0266.49036
[2] M. Giaquinta - L. PEPE, Esistenza e regolarità per il problema dell’area minima con ostacoli in n variabili , Ann. Sc. Norm. Sup. Pisa , 25 ( 1971 ), pp. 481 - 507 . Numdam | MR 305205 | Zbl 0283.49032 · Zbl 0283.49032
[3] H. Brezis - D. KINDERLEHRER, The smoothness of solution to nonlinear variational inequalities , Ind. Univ. Math. J. , 23 ( 1974 ), pp. 831 - 844 . MR 361436 | Zbl 0278.49011 · Zbl 0278.49011 · doi:10.1512/iumj.1974.23.23069
[4] U. Massari , Esistenza e regolarità delle ipersuperfici di curvatura media assegnata in Rn , Arch. Rat. Mech. Analysis , 55 ( 1974 ), pp. 357 - 382 . MR 355766 | Zbl 0305.49047 · Zbl 0305.49047 · doi:10.1007/BF00250439
[5] U. Massari , Frontiere orientate di curvatura media assegnata in Lp , Rend. Sem. Mat. Univ. Padova , 53 ( 1975 ), pp. 37 - 52 . Numdam | MR 417905 | Zbl 0358.49019 · Zbl 0358.49019
[6] E. De Giorgi - F. Colombini - L. Piccinini , Frontiere orientate di misura minima e questioni collegate , Pisa , Editrice Tecnico Scientifica ( 1972 ). Zbl 0296.49031 · Zbl 0296.49031
[7] M. Miranda , Un principio di massimo forte per le frontiere minimali ..., Rend. Sem. Mat. Univ. Padova , 45 ( 1971 ), pp. 355 - 366 . Numdam | MR 303390 | Zbl 0266.49034 · Zbl 0266.49034
[8] 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 . MR 74499 | Zbl 0066.29903 · Zbl 0066.29903
[9] I. Tamanini , Il problema della capillarità su domini non regolari , Rend. Sem. Mat. Univ. Padova , 56 ( 1977 ), pp. 169 - 191 . Numdam | MR 483992 | Zbl 0406.76031 · Zbl 0406.76031
[10] I. Tamanini : Boundaires of caccioppoli sets with hölder-continuous normal vector (to appear in j. reine angew, math. ). MR 667448 | Zbl 0479.49028 · Zbl 0479.49028 · doi:10.1515/crll.1982.334.27
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