Size minimization and approximating problems

Thierry De Pauw; Robert Hardt
August 2003
Calculus of Variations & Partial Differential Equations;Aug2003, Vol. 17 Issue 4, p405
Academic Journal
We consider Plateau type variational problems related to the size minimization of rectifiable currents. We realize the limit of a size minimizing sequence as a stationary varifold and a minimal set. Other examples of functionals to be minimized include the integral over the underlying carrying set of a power q of the multiplicity function, with $0 < q \leq 1$.Because minimizing sequences may have unbounded mass we make use of a more general object called a rectifiable scan for describing the limit. This concept is motivated by the possibility of recovering a flat chain from a sufficiently large collection of its slices. In case the given boundary is smooth and compact, the limiting scan has finite mass and corresponds to a rectifiable current.


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