Previous |  Up |  Next

Article

References:
[AH] Adams D. R., Hedberg L. I. : Function spaces and potential theory. Springer-Verlag, Berlin 1996. MR 1411441
[B] Bagby T. : Quasi topologies and rational approximation. J. Funct. Anal. 10 (1972), 259–268. MR 0355058 | Zbl 0266.30024
[BDG] Bombieri E., Giorgi E. De, Giusti E. : Minimal cones and the Bernstein problem. Invent. Math. 7 (1969), 255–267. MR 0250205 | Zbl 0183.25901
[BK] Brezis H., Kinderlehrer D. : The smoothness of solutions to nonlinear variational inequalities. Indiana Univ. Math. J. 23 (1974), 831–844. MR 0361436 | Zbl 0278.49011
[F1] Federer H. : Curvature measures. Trans. Amer. Math. Soc. 93 (1959), 418–491. MR 0110078 | Zbl 0089.38402
[F2] Federer H. : Geometric measure theory. Springer-Verlag, New York 1969. MR 0257325 | Zbl 0176.00801
[FR] Fleming W. H., Rishel R. : An integral formula for total gradient variation. Arch. Math. 11 (1960), 218–222. MR 0114892 | Zbl 0094.26301
[GZ] Gariepy R. F., Ziemer W. P. : Modern real analysis. PWS Publishing Co., 1994.
[GT] Gilbarg D., Trudinger N. : Elliptic partial differential equations of second order. Springer-Verlag, Second ed., New York 1983. MR 0737190 | Zbl 0562.35001
[G1] Giusti E. : Boundary behavior of nonparametric minimal surfaces. Indiana Univ. Math. J. 22 (1977), 435–444. MR 0305253
[G2] Giusti E. : Minimal surfaces and functions of bounded variation. Birkhäuser, 1985. MR 0775682
[GMT1] Gonzalez E., Massari U., Tamanini I. : Minimal boundaries enclosing a given volume. Manuscripta Math. 34 (1981), 381–395. MR 0620458 | Zbl 0481.49035
[GMT2] Gonzalez E., Massari U., Tamanini I. : On the regularity of sets minimizing perimeter with a volume constraint. Indiana Univ. Math. J. 32 (1983), 25–37. MR 0684753
[GH] Greenberg J. M., Harper J. R. : Algebraic topology. Benjamin-Cummings Press, 1981. Zbl 0498.55001
[Gr] Grüter M. : Boundary regularity for solutions of a partitioning problem. Arch. Rational Mech. Anal. 97 (1987), 261–270. MR 0862549 | Zbl 0613.49029
[H] Hardt R. : Uniqueness of nonparametric area minimizing currents. Indiana Univ. Math. J. 26 (1977), 65–71. MR 0451154 | Zbl 0333.49043
[Ha] Havin V. P. : Approximation in the mean by analytic functions. Soviet Math. Dokl. 9 (1968), 245–248.
[ISZ] Ilmanen T., Sternberg P., Ziemer W. : Equilibrium solutions to generalized motion by mean curvature. Accepted by J. Geom. Anal. MR 1731065 | Zbl 0941.35028
[KS] Kohn R. V., Strang G. : The constrained least gradient problem. Non-classical Continuum Mechanics. R. Knops and A. Lacy (eds.), Cambridge Univ. Press, 1987, 226–243. MR 0926504 | Zbl 0668.73060
[LS] Laurence P., Stredulinsky E. W. : On quasiconvex equimeasurable rearrangement, a counterexample and an example. J. Reine Angew. Math. 447 (1994), 63–81. MR 1263169 | Zbl 0848.35003
[MM] Massari U., Miranda M. : Minimal surfaces of codimension one. Mathematics Studies 91, North Holland, Amsterdam 1984. MR 0795963 | Zbl 0565.49030
[M] Miranda M. : Sul minimo dell’integrale del gradiente di una funzione. Ann. Scuola Norm. Sup. Pisa 19 (1965), 627–656. MR 0188839
[Mo] Moschen M. P. : Principio di massimo forte per le frontiere di misura minima. Ann. Univ. Ferrara Sez. VII, Sc. Mat. 23 (1977), 165–168. MR 0482508 | Zbl 0384.49030
[P1] Parks H. : Explicit determination of area minimizing hypersurfaces. Duke Math. J. 44 (1977), 519–534. MR 0458304 | Zbl 0385.49026
[P2] Parks H. : Explicit determination of area minimizing hypersurfaces, II. Mem. Amer. Math. Soc. 342 (1986). MR 0831890 | Zbl 0644.53007
[PZ] Parks H., Ziemer W. : Jacobi fields and functions of least gradient. Ann. Scuola Norm. Sup. Pisa XI (1984), 505–527. MR 0808421
[S1] Simon L. : Lectures on geometric measure theory. Proc. Centre Math. Analysis, ANU, Canberra, 3(1983). MR 0756417 | Zbl 0546.49019
[S2] Simon L. : A strict maximum principle for area minimizing hypersurfaces. J. Differential Geom. 26 (1987), 327–335. MR 0906394 | Zbl 0625.53052
[SWZ1] Sternberg P., Williams G., Ziemer W. : $C^{1,1}$ regularity of constrained area-minimizing hypersurfaces. J. Differential Equations 94 (1991), 83–94. MR 1133542
[SWZ2] Sternberg P., Williams G., Ziemer W. : Existence, uniqueness, and regularity for functions of least gradient. J. Reine Angew. Math. 430 (1992), 35–60. MR 1172906 | Zbl 0756.49021
[SWZ3] Sternberg P., Williams G., Ziemer W. : The constrained least gradient problem in $\mathbb R^{n}$. Trans. Amer. Math. Soc. 339 (1993), 403–433. MR 1126213
[SZ] Sternberg P., Ziemer W. : The Dirchlet problem for functions of least gradient. Invited paper to celebrate James Serrin’s $65^{\rm th}$ birthday. IMA Volumes in Math. and Appl. 47 (1993), 197–214. MR 1246349
[StZ] Stredulinsky E., Ziemer W. : Area minimizing sets subject to a volume constraint in a convex set. Accepted by J. Geom. Anal. MR 1669207 | Zbl 0940.49025
[SwZ] Swanson D., Ziemer W. : Sobolev functions whose inner trace at the boundary is zero. Accepted by Ark. Mat. MR 1714762 | Zbl 1021.46027
[T] Tamanini I. : Boundaries of Caccioppoli sets with Hölder-continuous normal vector. J. Reine Angew. Math. 334 (1982), 27–39. MR 0667448 | Zbl 0479.49028
[W] Williams G. : Regularity for solutions of the minimal surface equation with continuous boundary values. Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986), 411–429. MR 0870863 | Zbl 0627.49020
[Z] Ziemer W. P. : Weakly differentiable functions. Springer-Verlag, GTM Series, 120, Berlin 1989. MR 1014685 | Zbl 0692.46022
Partner of
EuDML logo