On local Lipschitz continuity of superposition operators

Gottfried Brückner

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Displaying similar documents to “On local Lipschitz continuity of superposition operators”

Local Lipschitz continuity of the stop operator

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On a closed convex set $Z$ in $ℝ^{N}$ with sufficiently smooth ( $𝒲^{2, \infty}$ ) boundary, the stop operator is locally Lipschitz continuous from $𝐖^{1, 1} ([0, T], ℝ^{N}) \times Z$ into $𝐖^{1, 1} ([0, T], ℝ^{N})$ . The smoothness of the boundary is essential: A counterexample shows that $𝒞^{1}$ -smoothness is not sufficient.

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