Traces of Sobolev spaces to irregular subsets of metric measure spaces
| Autor: | Tyulenev, Alexander |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Given $p \in (1,\infty)$, let $(\operatorname{X},\operatorname{d},\mu)$ be a metric measure space with uniformly locally doubling measure $\mu$ supporting a weak local $(1,p)$-Poincar\'e inequality. For each $\theta \in [0,p)$, we characterize the trace space of the Sobolev $W^{1}_{p}(\operatorname{X})$-space to lower codimension-$\theta$ content regular closed subsets $S \subset \operatorname{X}$. In particular, if the space $(\operatorname{X},\operatorname{d},\mu)$ is Ahlfors $Q$-regular for some $Q \geq 1$ and $p \in (Q,\infty)$, then we get an intrinsic description of the trace-space of the Sobolev $W^{1}_{p}(\operatorname{X})$-space to arbitrary closed nonempty set $S \subset \operatorname{X}$. Comment: Many typos in the previous versions have been corrected. Some proofs have been clarified |
| Databáze: | arXiv |
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