Regularity of gradient vector fields giving rise to finite Caccioppoli partitions

Roger Moser

doi:10.1007/s00526-022-02293-6

Regularity of gradient vector fields giving rise to finite Caccioppoli partitions

Roger Moser

Department of Mathematical Sciences

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Abstract

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.

Original language	English
Article number	183
Journal	Calculus of Variations and Partial Differential Equations
Volume	61
Issue number	5
DOIs	https://doi.org/10.1007/s00526-022-02293-6
Publication status	Published - 15 Jul 2022

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Publisher Copyright:
© 2022, The Author(s).

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "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. ",

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Regularity of gradient vector fields giving rise to finite Caccioppoli partitions

Abstract

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