Smooth homeomorphic approximation of piecewise affine homeomorphisms

Daniel Campbell; Filip Soudský

doi:10.4171/rlm/946

JournalsrlmVol. 32, No. 3pp. 511–534

Smooth homeomorphic approximation of piecewise affine homeomorphisms

Daniel Campbell
University of Hradec Králové; University of South Bohemia, Ceské Budejovice, Czechia
Filip Soudský
Technical University of Liberec; University of Hradec Králové, Czechia

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Abstract

Given any $f$ a locally finitely piecewise affine homeomorphism of $Ω \subset R^{n}$ onto $Δ \subset R^{n}$ in $W^{1, p}, 1 \leq p < \infty$ and any $ε > 0$ we construct a smooth injective map $\tilde{f}$ such that $∥ f - \tilde{f} ∥_{W^{1, p} (Ω, R^{n})} < ε$ .

Cite this article

Daniel Campbell, Filip Soudský, Smooth homeomorphic approximation of piecewise affine homeomorphisms. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 3, pp. 511–534

DOI 10.4171/RLM/946