Functions of least gradient and BV functions

Ziemer, William P.

  • Nonlinear Analysis, Function Spaces and Applications, Publisher: Czech Academy of Sciences, Mathematical Institute(Praha), page 270-312

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Ziemer, William P.. "Functions of least gradient and BV functions." Nonlinear Analysis, Function Spaces and Applications. Praha: Czech Academy of Sciences, Mathematical Institute, 1999. 270-312. <http://eudml.org/doc/221427>.

@inProceedings{Ziemer1999,
author = {Ziemer, William P.},
booktitle = {Nonlinear Analysis, Function Spaces and Applications},
keywords = {Spring school; Proceedings; Nonlinear analysis; Function spaces; Prague (Czech Republic)},
location = {Praha},
pages = {270-312},
publisher = {Czech Academy of Sciences, Mathematical Institute},
title = {Functions of least gradient and BV functions},
url = {http://eudml.org/doc/221427},
year = {1999},
}

TY - CLSWK
AU - Ziemer, William P.
TI - Functions of least gradient and BV functions
T2 - Nonlinear Analysis, Function Spaces and Applications
PY - 1999
CY - Praha
PB - Czech Academy of Sciences, Mathematical Institute
SP - 270
EP - 312
KW - Spring school; Proceedings; Nonlinear analysis; Function spaces; Prague (Czech Republic)
UR - http://eudml.org/doc/221427
ER -

References

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  1. Adams D. R., Hedberg L. I., Function spaces and potential theory, Springer-Verlag, Berlin 1996. (1996) MR1411441
  2. Bagby T., Quasi topologies and rational approximation, J. Funct. Anal. 10 (1972), 259–268. (1972) Zbl0266.30024MR0355058
  3. Bombieri E., Giorgi E. De, Giusti E., Minimal cones and the Bernstein problem, Invent. Math. 7 (1969), 255–267. (1969) Zbl0183.25901MR0250205
  4. Brezis H., Kinderlehrer D., The smoothness of solutions to nonlinear variational inequalities, Indiana Univ. Math. J. 23 (1974), 831–844. (1974) Zbl0278.49011MR0361436
  5. Federer H., Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418–491. (1959) Zbl0089.38402MR0110078
  6. Federer H., Geometric measure theory, Springer-Verlag, New York 1969. (1969) Zbl0176.00801MR0257325
  7. Fleming W. H., Rishel R., An integral formula for total gradient variation, Arch. Math. 11 (1960), 218–222. (1960) Zbl0094.26301MR0114892
  8. Gariepy R. F., Ziemer W. P., Modern real analysis, PWS Publishing Co., 1994. (1994) 
  9. Gilbarg D., Trudinger N., Elliptic partial differential equations of second order, Springer-Verlag, Second ed., New York 1983. (1983) Zbl0562.35001MR0737190
  10. Giusti E., Boundary behavior of nonparametric minimal surfaces, Indiana Univ. Math. J. 22 (1977), 435–444. (1977) MR0305253
  11. Giusti E., Minimal surfaces and functions of bounded variation, Birkhäuser, 1985. (1985) MR0775682
  12. Gonzalez E., Massari U., Tamanini I., Minimal boundaries enclosing a given volume, Manuscripta Math. 34 (1981), 381–395. (1981) Zbl0481.49035MR0620458
  13. 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. (1983) MR0684753
  14. Greenberg J. M., Harper J. R., Algebraic topology, Benjamin-Cummings Press, 1981. (1981) Zbl0498.55001
  15. Grüter M., Boundary regularity for solutions of a partitioning problem, Arch. Rational Mech. Anal. 97 (1987), 261–270. (1987) Zbl0613.49029MR0862549
  16. Hardt R., Uniqueness of nonparametric area minimizing currents, Indiana Univ. Math. J. 26 (1977), 65–71. (1977) Zbl0333.49043MR0451154
  17. Havin V. P., Approximation in the mean by analytic functions, Soviet Math. Dokl. 9 (1968), 245–248. (1968) 
  18. Ilmanen T., Sternberg P., Ziemer W., Equilibrium solutions to generalized motion by mean curvature, Accepted by J. Geom. Anal. Zbl0941.35028MR1731065
  19. 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. (1987) Zbl0668.73060MR0926504
  20. Laurence P., Stredulinsky E. W., On quasiconvex equimeasurable rearrangement, a counterexample and an example, J. Reine Angew. Math. 447 (1994), 63–81. (1994) Zbl0848.35003MR1263169
  21. Massari U., Miranda M., Minimal surfaces of codimension one, Mathematics Studies 91, North Holland, Amsterdam 1984. (1984) Zbl0565.49030MR0795963
  22. Miranda M., Sul minimo dell’integrale del gradiente di una funzione, Ann. Scuola Norm. Sup. Pisa 19 (1965), 627–656. (1965) MR0188839
  23. Moschen M. P., Principio di massimo forte per le frontiere di misura minima, Ann. Univ. Ferrara Sez. VII, Sc. Mat. 23 (1977), 165–168. (1977) Zbl0384.49030MR0482508
  24. Parks H., Explicit determination of area minimizing hypersurfaces, Duke Math. J. 44 (1977), 519–534. (1977) Zbl0385.49026MR0458304
  25. Parks H., Explicit determination of area minimizing hypersurfaces, II, Mem. Amer. Math. Soc. 342 (1986). (1986) Zbl0644.53007MR0831890
  26. Parks H., Ziemer W., Jacobi fields and functions of least gradient, Ann. Scuola Norm. Sup. Pisa XI (1984), 505–527. (1984) MR0808421
  27. Simon L., Lectures on geometric measure theory, Proc. Centre Math. Analysis, ANU, Canberra, 3(1983). (1983) Zbl0546.49019MR0756417
  28. Simon L., A strict maximum principle for area minimizing hypersurfaces, J. Differential Geom. 26 (1987), 327–335. (1987) Zbl0625.53052MR0906394
  29. Sternberg P., Williams G., Ziemer W., C 1 , 1 regularity of constrained area-minimizing hypersurfaces, J. Differential Equations 94 (1991), 83–94. (1991) MR1133542
  30. Sternberg P., Williams G., Ziemer W., Existence, uniqueness, and regularity for functions of least gradient, J. Reine Angew. Math. 430 (1992), 35–60. (1992) Zbl0756.49021MR1172906
  31. Sternberg P., Williams G., Ziemer W., The constrained least gradient problem in n , Trans. Amer. Math. Soc. 339 (1993), 403–433. (1993) MR1126213
  32. Sternberg P., Ziemer W., The Dirchlet problem for functions of least gradient, Invited paper to celebrate James Serrin’s birthday. IMA Volumes in Math. and Appl. 47 (1993), 197–214. (1993) MR1246349
  33. Stredulinsky E., Ziemer W., Area minimizing sets subject to a volume constraint in a convex set, Accepted by J. Geom. Anal. Zbl0940.49025MR1669207
  34. Swanson D., Ziemer W., Sobolev functions whose inner trace at the boundary is zero, Accepted by Ark. Mat. Zbl1021.46027MR1714762
  35. Tamanini I., Boundaries of Caccioppoli sets with Hölder-continuous normal vector, J. Reine Angew. Math. 334 (1982), 27–39. (1982) Zbl0479.49028MR0667448
  36. 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. (1986) Zbl0627.49020MR0870863
  37. Ziemer W. P., Weakly differentiable functions, Springer-Verlag, GTM Series, 120, Berlin 1989. (1989) Zbl0692.46022MR1014685

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