| Title:
|
Functions of least gradient and BV functions (English) |
| Author:
|
Ziemer, William P. |
| Language:
|
English |
| Journal:
|
Nonlinear Analysis, Function Spaces and Applications |
| Volume:
|
Vol. 6 |
| Issue:
|
1998 |
| Year:
|
|
| Pages:
|
270-312 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26B30 |
| MSC:
|
46E35 |
| MSC:
|
46E99 |
| MSC:
|
49Q05 |
| MSC:
|
49Q20 |
| MSC:
|
58E12 |
| idZBL:
|
Zbl 0965.46023 |
| idMR:
|
MR1777718 |
| . |
| Date available:
|
2009-10-08T09:48:20Z |
| Last updated:
|
2012-08-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702475 |
| . |
| Reference:
|
[AH] Adams D. R., Hedberg L. I. : Function spaces and potential theory.Springer-Verlag, Berlin 1996. MR 1411441 |
| Reference:
|
[B] Bagby T. : Quasi topologies and rational approximation.J. Funct. Anal. 10 (1972), 259–268. Zbl 0266.30024, MR 0355058 |
| Reference:
|
[BDG] Bombieri E., Giorgi E. De, Giusti E. : Minimal cones and the Bernstein problem.Invent. Math. 7 (1969), 255–267. Zbl 0183.25901, MR 0250205 |
| Reference:
|
[BK] Brezis H., Kinderlehrer D. : The smoothness of solutions to nonlinear variational inequalities.Indiana Univ. Math. J. 23 (1974), 831–844. Zbl 0278.49011, MR 0361436 |
| Reference:
|
[F1] Federer H. : Curvature measures.Trans. Amer. Math. Soc. 93 (1959), 418–491. Zbl 0089.38402, MR 0110078 |
| Reference:
|
[F2] Federer H. : Geometric measure theory.Springer-Verlag, New York 1969. Zbl 0176.00801, MR 0257325 |
| Reference:
|
[FR] Fleming W. H., Rishel R. : An integral formula for total gradient variation.Arch. Math. 11 (1960), 218–222. Zbl 0094.26301, MR 0114892 |
| Reference:
|
[GZ] Gariepy R. F., Ziemer W. P. : Modern real analysis.PWS Publishing Co., 1994. |
| Reference:
|
[GT] Gilbarg D., Trudinger N. : Elliptic partial differential equations of second order.Springer-Verlag, Second ed., New York 1983. Zbl 0562.35001, MR 0737190 |
| Reference:
|
[G1] Giusti E. : Boundary behavior of nonparametric minimal surfaces.Indiana Univ. Math. J. 22 (1977), 435–444. MR 0305253 |
| Reference:
|
[G2] Giusti E. : Minimal surfaces and functions of bounded variation.Birkhäuser, 1985. MR 0775682 |
| Reference:
|
[GMT1] Gonzalez E., Massari U., Tamanini I. : Minimal boundaries enclosing a given volume.Manuscripta Math. 34 (1981), 381–395. Zbl 0481.49035, MR 0620458 |
| Reference:
|
[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 |
| Reference:
|
[GH] Greenberg J. M., Harper J. R. : Algebraic topology.Benjamin-Cummings Press, 1981. Zbl 0498.55001 |
| Reference:
|
[Gr] Grüter M. : Boundary regularity for solutions of a partitioning problem.Arch. Rational Mech. Anal. 97 (1987), 261–270. Zbl 0613.49029, MR 0862549 |
| Reference:
|
[H] Hardt R. : Uniqueness of nonparametric area minimizing currents.Indiana Univ. Math. J. 26 (1977), 65–71. Zbl 0333.49043, MR 0451154 |
| Reference:
|
[Ha] Havin V. P. : Approximation in the mean by analytic functions.Soviet Math. Dokl. 9 (1968), 245–248. |
| Reference:
|
[ISZ] Ilmanen T., Sternberg P., Ziemer W. : Equilibrium solutions to generalized motion by mean curvature.Accepted by J. Geom. Anal. Zbl 0941.35028, MR 1731065 |
| Reference:
|
[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. Zbl 0668.73060, MR 0926504 |
| Reference:
|
[LS] Laurence P., Stredulinsky E. W. : On quasiconvex equimeasurable rearrangement, a counterexample and an example.J. Reine Angew. Math. 447 (1994), 63–81. Zbl 0848.35003, MR 1263169 |
| Reference:
|
[MM] Massari U., Miranda M. : Minimal surfaces of codimension one.Mathematics Studies 91, North Holland, Amsterdam 1984. Zbl 0565.49030, MR 0795963 |
| Reference:
|
[M] Miranda M. : Sul minimo dell’integrale del gradiente di una funzione.Ann. Scuola Norm. Sup. Pisa 19 (1965), 627–656. MR 0188839 |
| Reference:
|
[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. Zbl 0384.49030, MR 0482508 |
| Reference:
|
[P1] Parks H. : Explicit determination of area minimizing hypersurfaces.Duke Math. J. 44 (1977), 519–534. Zbl 0385.49026, MR 0458304 |
| Reference:
|
[P2] Parks H. : Explicit determination of area minimizing hypersurfaces, II.Mem. Amer. Math. Soc. 342 (1986). Zbl 0644.53007, MR 0831890 |
| Reference:
|
[PZ] Parks H., Ziemer W. : Jacobi fields and functions of least gradient.Ann. Scuola Norm. Sup. Pisa XI (1984), 505–527. MR 0808421 |
| Reference:
|
[S1] Simon L. : Lectures on geometric measure theory.Proc. Centre Math. Analysis, ANU, Canberra, 3(1983). Zbl 0546.49019, MR 0756417 |
| Reference:
|
[S2] Simon L. : A strict maximum principle for area minimizing hypersurfaces.J. Differential Geom. 26 (1987), 327–335. Zbl 0625.53052, MR 0906394 |
| Reference:
|
[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 |
| Reference:
|
[SWZ2] Sternberg P., Williams G., Ziemer W. : Existence, uniqueness, and regularity for functions of least gradient.J. Reine Angew. Math. 430 (1992), 35–60. Zbl 0756.49021, MR 1172906 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[StZ] Stredulinsky E., Ziemer W. : Area minimizing sets subject to a volume constraint in a convex set.Accepted by J. Geom. Anal. Zbl 0940.49025, MR 1669207 |
| Reference:
|
[SwZ] Swanson D., Ziemer W. : Sobolev functions whose inner trace at the boundary is zero.Accepted by Ark. Mat. Zbl 1021.46027, MR 1714762 |
| Reference:
|
[T] Tamanini I. : Boundaries of Caccioppoli sets with Hölder-continuous normal vector.J. Reine Angew. Math. 334 (1982), 27–39. Zbl 0479.49028, MR 0667448 |
| Reference:
|
[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. Zbl 0627.49020, MR 0870863 |
| Reference:
|
[Z] Ziemer W. P. : Weakly differentiable functions.Springer-Verlag, GTM Series, 120, Berlin 1989. Zbl 0692.46022, MR 1014685 |
| . |
