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A variational problem involving the distributional determinant. (English) Zbl 1222.49056
Summary: We deal with bounded \(W^{1,n-1}\)-maps defined in \(n\)-dimensional domains, whose graph has finite area and finite boundary mass. We show that the singular part of the distributional determinant is concentrated on a countable set of points. A related variational problem is then considered. Finally, we study the analogous problem involving the distributional minors of fixed order.

MSC:
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
28A75 Length, area, volume, other geometric measure theory
49J52 Nonsmooth analysis
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