TY - JOUR
T1 - Regularity of gradient vector fields giving rise to finite Caccioppoli partitions
AU - Moser, Roger
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/7/15
Y1 - 2022/7/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85134225221&partnerID=8YFLogxK
U2 - 10.1007/s00526-022-02293-6
DO - 10.1007/s00526-022-02293-6
M3 - Article
SN - 0944-2669
VL - 61
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 5
M1 - 183
ER -