Publications
William P. Ziemer
- Gui-Qiang Chen and
Monica Torres and
William P. Ziemer, Gauss-Green theorem for weakly
differentiable vector fields,
sets of finite perimeter, and balance laws,
[ PDF ]
-
William P. Ziemer, The Gauss-Green theorem for weakly
differentiable vector Fields
to appear in the proceedings of a
conference on a Workshop on singularities in PDE and the Calculus
of variations, which was held at the Centre of recherche math
antiques Universite de Montreal, July 17-21, 2006.
[ PDF ]
- Jan Maly, David Swanson, and
William P. Ziemer. Fine behavior of functions with
gradients in a Lorentz space,
Submitted for publication.
- Swanson, David and Ziemer,
William P., The image of a weakly differentiable mapping, SIAM
Analysis, 35(2004), 1099 -1109.
- Montero, Alberto, and
Sternberg, Peter and Ziemer, William P. Local minimizers with vortices to
the Ginzburg Landau system Comm. Pure and Appl. Math. ,
LVII(2004):99-125.
[ DVI ]
- Jan Maly, David Swanson, and
William P. Ziemer. The co-area formula for Sobolev mappings. Trans.
Amer. Math. Soc., 355(2):477-492 (electronic), 2003.
[ PDF ]
- David Swanson and
William P. Ziemer. A topological aspect of Sobolev mappings. Calc.
Var. Partial Differential Equations, 14(1):69-84, 2002.
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- William P. Ziemer and
Kevin Zumbrun. The obstacle problem for functions of least gradient. Math.
Bohem., 124(2-3):193-219, 1999.
[ DVI ] [ PDF]
- William P. Ziemer.
Functions of least gradient and BV functions. In Nonlinear analysis,
function spaces and applications, Vol. 6 (Prague, 1998), pages 270-312. Acad.
Sci. Czech Repub., Prague,
1999.
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- David Swanson and
William P. Ziemer. Sobolev functions whose inner trace at the
boundary is zero. Ark.
Mat., 37(2):373-380, 1999.
[ DVI ]
- Tom Ilmanen, Peter Sternberg,
and William P. Ziemer. Equilibrium solutions to generalized motion by
mean curvature. J. Geom. Anal., 8(5):845-858, 1998. Dedicated to
the memory of Fred Almgren.
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- Edward Stredulinsky and
William P. Ziemer. Area minimizing sets subject to a volume
constraint in a convex set. J. Geom. Anal., 7(4):653-677, 1997.
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- Jan Maly and William P.
Ziemer. Fine regularity of solutions of elliptic partial differential
equations, volume 51 of Mathematical Surveys and Monographs.
American Mathematical Society, Providence,
RI, 1997.
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- Peter Sternberg and
William P. Ziemer. Local minimisers of a three-phase partition
problem with triple junctions. Proc. Roy. Soc. Edinburgh Sect. A,
124(6):1059-1073, 1994.
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- Peter Sternberg and
William P. Ziemer. Generalized motion by curvature with a Dirichlet
condition. J. Differential Equations, 114(2):580-600, 1994.
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- Peter Sternberg and
William P. Ziemer. The Dirichlet problem for functions of least
gradient. In Degenerate diffusions (Minneapolis, MN, 1991),
volume 47 of IMA Vol. Math. Appl., pages 197-214. Springer, New York, 1993.
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- L. D. Berkovitz,
Steven E. Shreve, and William P. Ziemer. A tribute to Wendell H.
Fleming. SIAM
J. Control Optim., 31(2):273-281, 1993.
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- Peter Sternberg, Graham
Williams, and William P. Ziemer. The constrained least gradient
problem in R n. Trans. Amer. Math. Soc.,
339(1):403-432, 1993.
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- O. Martio and
William P. Ziemer. Lusin's condition (N) and mappings with
nonnegative Jacobians. Michigan
Math. J., 39(3):495-508, 1992.
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- Peter Sternberg, Graham
Williams, and William P. Ziemer. Existence, uniqueness, and
regularity for functions of least gradient. J. Reine Angew. Math.,
430:35-60, 1992.
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- W. P. Ziemer.
Variational inequalities with degenerate elliptic operators. In Differential
equations and its applications (Budapest,
1991), volume 62 of Colloq. Math. Soc. János Bolyai, pages
359-396. North-Holland, Amsterdam,
1991.
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- Peter Sternberg,
William P. Ziemer, and Graham Williams. C 1,1-regularity of
constrained area minimizing hypersurfaces. J. Differential Equations,
94(1):83-94, 1991.
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- Tero Kilpeläinen and
William P. Ziemer. Pointwise regularity of solutions to nonlinear
double obstacle problems. Ark.
Mat., 29(1):83-106, 1991.
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- J. H. Michael and
William P. Ziemer. Existence of solutions to obstacle problems. Nonlinear
Anal., 17(1):45-71, 1991.
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- Jun Mu and William P.
Ziemer. Smooth regularity of solutions of double obstacle problems
involving degenerate elliptic equations. Comm. Partial Differential
Equations, 16(4-5):821-843, 1991.
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- J.-M. Rakotoson and
William P. Ziemer. Local behavior of solutions of quasilinear
elliptic equations with general structure. Trans. Amer. Math. Soc.,
319(2):747-764, 1990.
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- William P. Ziemer. Weakly
differentiable functions, volume 120 of Graduate Texts in
Mathematics. Springer-Verlag,
New York, 1989. Sobolev
spaces and functions of bounded variation.
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- William P. Ziemer.
Uniform differentiability of Sobolev functions. Indiana Univ.
Math. J., 37(4):789-799, 1988.
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- William P. Ziemer.
Regularity of weak solutions of parabolic variational inequalities. Trans.
Amer. Math. Soc., 309(2):763-786, 1988.
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- John E. Brothers and
William P. Ziemer. Minimal rearrangements of Sobolev functions. J.
Reine Angew. Math., 384:153-179, 1988.
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- John E. Brothers and
William P. Ziemer. Minimal rearrangements of Sobolev functions. Acta Univ. Carolin. Math. Phys.,
28(2):13-24, 1987. 15th winter school in abstract analysis (Srní, 1987).
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- J. H. Michael and
William P. Ziemer. The Wiener criterion and quasilinear uniformly
elliptic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire,
4(5):453-486, 1987.
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- J. H. Michael and
William P. Ziemer. Interior regularity for solutions to obstacle
problems. Nonlinear Anal., 10(12):1427-1448, 1986.
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- William P. Ziemer.
Regularity of quasiminima and obstacle problems. In Geometric measure
theory and the calculus of variations (Arcata, Calif., 1984),
volume 44 of Proc. Sympos. Pure Math., pages 429-439. Amer.
Math. Soc., Providence,
RI, 1986.
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- William P. Ziemer. A
Poincaré-type inequality for solutions of elliptic differential equations.
Proc. Amer. Math. Soc., 97(2):286-290, 1986.
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- William P. Ziemer.
Boundary regularity for quasiminima. Arch. Rational Mech. Anal.,
92(4):371-382, 1986.
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- Morton E. Gurtin,
William O. Williams, and William P. Ziemer. Geometric measure
theory and the axioms of continuum thermodynamics. Arch. Rational Mech.
Anal., 92(1):1-22, 1986.
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- J. H. Michael and
William P. Ziemer. A Lusin type approximation of Sobolev functions by
smooth functions. In Classical real analysis (Madison, Wis., 1982),
volume 42 of Contemp. Math., pages 135-167. Amer. Math. Soc., Providence, RI,
1985.
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- Harold R. Parks and
William P. Ziemer. Jacobi fields and regularity of functions of least
gradient. Ann. Scuola Norm. Sup. Pisa
Cl. Sci. (4), 11(4):505-527, 1984.
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- William P. Ziemer.
Smooth foliations generated by functions of least gradient. In Miniconference
on nonlinear analysis (Canberra,
1984), volume 8 of Proc. Centre Math. Anal. Austral. Nat.
Univ., pages 84-90. Austral. Nat. Univ., Canberra, 1984.
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- William P. Ziemer.
Cauchy flux and sets of finite perimeter. Arch. Rational Mech. Anal.,
84(3):189-201, 1983.
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- William P. Ziemer. Mean
values of subsolutions of elliptic and parabolic equations. Trans.
Amer. Math. Soc., 279(2):555-568, 1983.
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- William P. Ziemer.
Regularity at the boundary and removable singularities for solutions of
quasilinear parabolic equations. In Miniconference on partial
differential equations (Canberra,
1981), volume 1 of Proc. Centre Math. Anal. Austral. Nat.
Univ., pages 17-25. Austral. Nat. Univ., Canberra, 1982.
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- Ronald Gariepy and
William P. Ziemer. Thermal capacity and boundary regularity. J.
Differential Equations, 45(3):374-388, 1982.
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- William P. Ziemer.
Interior and boundary continuity of weak solutions of degenerate parabolic
equations. Trans. Amer. Math. Soc., 271(2):733-748, 1982.
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- Ronald Gariepy and
William P. Ziemer. Removable sets for quasilinear parabolic
equations. J. London Math. Soc. (2), 21(2):311-318, 1980.
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- William P. Ziemer.
Behavior at the boundary of solutions of quasilinear parabolic equations. J.
Differential Equations, 35(3):291-305, 1980.
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- J. H. Ewing, W. H.
Gustafson, P. R. Halmos, S. H. Moolgavkar, W. H. Wheeler,
and W. P. Ziemer. American mathematics from 1940 to the day before
yesterday. Pokroky Mat. Fyz. Astronom., 24(6):326-335, 1979.
Translated from the English by Jirí Vanzura.
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- J. H. Ewing, W. H.
Gustafson, P. R. Halmos, S. H. Moolgavkar, W. H. Wheeler,
and W. P. Ziemer. American mathematics from 1940 to the day before
yesterday. Pokroky Mat. Fyz. Astronom., 24(5):258-267, 1979.
Translated from the English by Jirí Vanzur.
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- William P. Ziemer. The
Dirichlet problem for Euler-Lagrange equations on arbitrary domains. J.
London Math. Soc. (2), 19(3):481-487, 1979.
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- Norman G. Meyers and
William P. Ziemer. Integral inequalities of Poincaré and Wirtinger
type for BV functions. Amer. J. Math., 99(6):1345-1360, 1977.
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- Ronald Gariepy and
William P. Ziemer. A regularity condition at the boundary for
solutions of quasilinear elliptic equations. Arch. Rational Mech. Anal.,
67(1):25-39, 1977.
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- William P. Ziemer. Some
remarks on harmonic measure in space. Pacific J. Math., 55:629-637,
1974.
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- Ronald Gariepy and
William P. Ziemer. Behavior at the boundary of solutions of
quasilinear elliptic equations. Arch. Rational Mech. Anal.,
56:372-384, 1974/75.
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- Thomas Bagby and
William P. Ziemer. Pointwise differentiability and absolute
continuity. Trans. Amer. Math. Soc., 191:129-148, 1974.
[PDF ]
- Herbert Federer and
William P. Ziemer. The Lebesgue set of a function whose distribution
derivatives are p-th power summable. Indiana Univ.
Math. J., 22:139-158, 1972/73.
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- W. D. Pepe and
William P. Ziemer. Slices, multiplicity, and Lebesgue area. Pacific
J. Math., 43:701-710, 1972.
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- William P. Ziemer.
Slices of maps and Lebesgue area. Trans. Amer. Math. Soc.,
164:139-151, 1972.
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- Casper Goffman and William P.
Ziemer. Higher dimensional mappings for which the area formula holds. Ann.
of Math. (2), 92:482-488, 1970.
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- William P. Ziemer.
Extremal length as a capacity. Michigan
Math. J., 17:117-128, 1970.
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- Casper Goffman and William P.
Ziemer. Higher dimensional mappings for which the area formula holds. Proc.
Nat. Acad. Sci. U.S.A., 65:491-494, 1970.
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- William P. Ziemer.
Extremal length and p-capacity. Michigan Math. J.,
16:43-51, 1969.
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- William P. Ziemer.
Change of variables for absolutely continuous functions. Duke Math. J.,
36:171-178, 1969.
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- William P. Ziemer. The
area and variation of linearly continuous functions. Proc. Amer. Math.
Soc., 20:81-87, 1969.
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- William P. Ziemer.
Extremal length and conformal capacity. Trans. Amer. Math. Soc.,
126:460-473, 1967.
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- William P. Ziemer. Some
lower bounds for Lebesgue area. Pacific J. Math., 19:381-390, 1966.
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- William P. Ziemer. The
structure of quasi-open maps. Duke Math. J., 32:661-671, 1965.
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- William P. Ziemer. On a
sufficient condition of onto-ness. J. Math. Mech., 13:503-509,
1964.
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- William P. Ziemer. On
the compactness of integral classes. Pacific J. Math.,
13:1437-1451, 1963.
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- Robert J. Troyer and
William P. Ziemer. Topologies generated by outer measures. J.
Math. Mech., 12:485-494, 1963.
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- William P. Ziemer.
Integral currents mod 2. Trans. Amer. Math. Soc.,
105:496-524, 1962.
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