13 citations · 15 across the 4 of their papers we have counts for
5 papers
Aspects of area formulas by way of Luzin, Radó, and Reichelderfer on metric measure spaces
Niko Marola, William P. Ziemer
We consider some measure-theoretic properties of functions belonging to a Sobolev-type class on metric measure spaces that admit a Poincaré inequality and are equipped with a doubl…
Gauss-Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws
G. Q. Chen, M. Torres, W. Ziemer
We analyze a class of weakly differentiable vector fields (\FF \colon \rn \to \rn) with the property that (\FF\in L^{\infty}) and (÷\FF) is a Radon measure. The primary focus of ou…
The coarea formula for Sobolev mappings
Jan Maly, David Swanson, William P. Ziemer
We extend Federer's coarea formula to mappings belonging to the Sobolev class , , , and more generally, to mappings with gradient in the Lor…
Area Minimizing Sets Subject to a Volume Constraint in a Convex Set
Edward Stredulinsky, William P. Ziemer
In this paper we consider the problem of minimizing area subject to a volume constraint in a given convex set.
The Obstacle Problem for Functions of Least Gradient
William P. Ziemer, Kevin Zumbrun
For a given domain , we consider the variational problem of minimizing the -norm of the gradient on of a function with prescribed continuous bounda…