Sobolev Embedding Theorem for Irregular Domains and Discontinuity of $p \to p^*(p,n)$

Tomáš G. Roskovec

doi:10.4171/zaa/1558

JournalszaaVol. 35, No. 2pp. 139–152

Sobolev Embedding Theorem for Irregular Domains and Discontinuity of $p \to p^{*} (p, n)$

Tomáš G. Roskovec
Charles University, Prague, Czech Republic

$Sobolev Embedding Theorem for Irregular Domains and Discontinuity of $p \to p^*(p,n)$ cover$

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Abstract

For a domain $Ω \subset R^{n}$ we denote

q_{Ω} (p) := sup {r \in [1, \infty]; for all f : Ω \to R : (f \in W^{1, p} (Ω) \Rightarrow f \in L^{r} (Ω))} .

Let $p_{0} \in [2, \infty) .$ We construct a domain $Ω \subset R^{2}$ such that $q_{Ω} (p)$ is discontinuous at $p_{0} .$

Cite this article

Tomáš G. Roskovec, Sobolev Embedding Theorem for Irregular Domains and Discontinuity of $p \to p^{*} (p, n)$ . Z. Anal. Anwend. 35 (2016), no. 2, pp. 139–152

DOI 10.4171/ZAA/1558