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Consider a function u ∈ BV ² _loc(R ² such that ∇u takes values in a fixed set of three vectors almost everywhere. This condition implies that u is piecewise affine away from a closed set of...

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...

Motivated by the harmonic map heat flow, we consider maps between Riemannian manifolds such that the tension field belongs to an L^p-space. Under an appropriate smallness condition, a certain degree of regularity...

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...

Motivated by the harmonic map heat flow, we consider maps between Riemannian manifolds such that the tension field belongs to an L^p-space. Under an appropriate smallness condition, a certain degree of regularity...

Consider a function u ∈ BV ² _loc(R ² such that ∇u takes values in a fixed set of three vectors almost everywhere. This condition implies that u is piecewise affine away from a closed set of...

We study a variational model for transition layers with an underlying functional that combines an Allen-Cahn type structure with an additional nonlocal interaction term. A transition layer is represented by a map from R to S...