**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Rellich–Kondrachov theorem

Summary

In mathematics, the Rellich–Kondrachov theorem is a compact embedding theorem concerning Sobolev spaces. It is named after the Austrian-German mathematician Franz Rellich and the Russian mathematician Vladimir Iosifovich Kondrashov. Rellich proved the L2 theorem and Kondrashov the Lp theorem.
Statement of the theorem
Let Ω ⊆ Rn be an open, bounded Lipschitz domain, and let 1 ≤ p < n. Set
:p^{*} := \frac{n p}{n - p}.
Then the Sobolev space W1,p(Ω; R) is continuously embedded in the Lp space Lp∗(Ω; R) and is compactly embedded in Lq(Ω; R) for every 1 ≤ q < p∗. In symbols,
:W^{1, p} (\Omega) \hookrightarrow L^{p^{*}} (\Omega)
and
:W^{1, p} (\Omega) \subset \subset L^{q} (\Omega) \text{ for } 1 \leq q < p^{*}.
Kondrachov embedding theorem
On a compact manifold with C1 boundary, the Kondrachov embedding theorem states that if k > ℓ and k − n/p > ℓ − n/q t

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related publications

Related people

Related units

No results

No results

No results

Related concepts

Related lectures

Related courses

No results

No results

No results