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arXiv · 2005.04998

Diffeomorphic approximation of Planar Sobolev Homeomorphisms in rearrangement invariant spaces

Daniel Campbell·Luigi Greco·Roberta Schiattarella·Filip Soudsky
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Abstract

Let $\Omega\subseteq\mathcal{R}^2$ be a domain, let $X$ be a rearrangement invariant space and let $f\in W^{1}X(\Omega,\mathcal{R}^2)$ be a homeomorphism between $\Omega$ and $f(\Omega)$. Then there exists a sequence of diffeomorphisms $f_k$ converging to $f$ in the space $W^{1}X(\Omega,\mathcal{R}^2)$.

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Daniel Campbell, Luigi Greco, Roberta Schiattarella, Filip Soudsky. 2020-05-11. Diffeomorphic approximation of Planar Sobolev Homeomorphisms in rearrangement invariant spaces. https://arxiv.org/abs/2005.04998

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