For a finite set A⊆ R n, consider a function u∈BVloc2(Rn) such that ∇ u∈ A almost everywhere. If A is convex independent, then it follows that u is piecewise affine away from a closed, countably H n - 1-rectifiable set. If A is affinely independent, then u is piecewise affine away from a closed H n - 1-null set.
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 15 Jul 2022|
ASJC Scopus subject areas
- Applied Mathematics