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arXiv · 1811.01576

Sharp estimates for approximation numbers of non-periodic Sobolev embeddings

Therese Mieth
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Abstract

We investigate asymptotically sharp upper and lower bounds for the approximation numbers of the compact Sobolev embeddings $\overset{\circ}{W}{^m}(\Omega)\hookrightarrow L_2(\Omega)$ and $ W^m(\Omega)\hookrightarrow L_2(\Omega)$, defined on a bounded domain $\Omega\subset\mathbb{R}^d$, involving explicit constants depending on $m$ and $d$. The key of proof is to relate the approximation problems to certain Dirichlet and Neumann eigenvalue problems.

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Therese Mieth. 2018-11-05. Sharp estimates for approximation numbers of non-periodic Sobolev embeddings. https://arxiv.org/abs/1811.01576

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