arXiv subjects

Therese Mieth

Publications and source records attributed to Therese Mieth.

2 recordsLinked to original sources

arXiv2018

Sharp estimates for approximation numbers of non-periodic Sobolev embeddings

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.

math.FA↗

arXiv2015

Entropy and approximation numbers of weighted Sobolev spaces via bracketing

We investigate the asymptotic behaviour of entropy and approximation numbers of the compact embedding $E^m_{p,σ}(B)\hookrightarrow L_p(B)$, $1\leq p<\infty,$ defined on the unit ball $B$ in $\mathbb{R}^n$. Here $E^m_{p,σ}(B)$ denotes a Sobolev space with a power weight perturbed by a logarithmic function. The weight contains a singularity at the origin. Inspired by Evans and Harris, we apply a bracketing technique which is an analogue to that of Dirichlet-Neumann-bracketing used by Triebel if $p=2$.

math.FA↗