Sobolev inequality

Sobolev inequality - theorem about inclusions between Sobolev spaces: if 1≤r≤s<∞ and 1/r − k/n = 1/s − l/n, then Wᵏʳ(ℝⁿ) ⊆ Wˡˢ(ℝⁿ). Article “Sobolev inequality” in English Wikipedia has 35.6 points for quality (as of July 1, 2025). The article contains 5 references and 13 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that (English) language version.

Since the creation of article “Sobolev inequality”, its content was written by 63 registered users of English Wikipedia and edited by 116 registered Wikipedia users in all languages.

The article is cited 143 times in English Wikipedia and cited 207 times in all languages.

The highest Authors Interest rank from 2001:

• Local (English): #55863 in July 2009
• Global: #103856 in May 2023

The highest popularity rank from 2008:

• Local (English): #200910 in March 2015
• Global: #313713 in May 2025

There are 6 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

#	Language	Quality grade	Quality score
1	English (en) Sobolev inequality		35.6333
2	Chinese (zh) 索博列夫不等式		32.1079
3	Catalan (ca) Desigualtat de Sobolev		16.6076
4	Italian (it) Disuguaglianza di Sobolev		11.7819
5	Japanese (ja) ソボレフ不等式		10.3582
6	French (fr) Injections de Sobolev		6.1632

More...

The following table shows the most popular language versions of the article.

The most popular language versions of the article "Sobolev inequality" in all the time

#	Language	Popularity award	Relative popularity
1	English (en) Sobolev inequality		702 400
2	Italian (it) Disuguaglianza di Sobolev		35 872
3	Japanese (ja) ソボレフ不等式		29 175
4	Chinese (zh) 索博列夫不等式		11 707
5	French (fr) Injections de Sobolev		6 680
6	Catalan (ca) Desigualtat de Sobolev		39

More...

The following table shows the language versions of the article with the highest popularity in the last month.

The most popular language versions of the article "Sobolev inequality" in June 2025

#	Language	Popularity award	Relative popularity
1	English (en) Sobolev inequality		4 541
2	Japanese (ja) ソボレフ不等式		296
3	French (fr) Injections de Sobolev		258
4	Italian (it) Disuguaglianza di Sobolev		188
5	Chinese (zh) 索博列夫不等式		184
6	Catalan (ca) Desigualtat de Sobolev		3

More...

The following table shows the language versions of the article with the highest Authors’ Interest.

Language versions of the article "Sobolev inequality" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.

#	Language	AI award	Relative AI
1	English (en) Sobolev inequality		63
2	Italian (it) Disuguaglianza di Sobolev		24
3	French (fr) Injections de Sobolev		13
4	Japanese (ja) ソボレフ不等式		8
5	Chinese (zh) 索博列夫不等式		6
6	Catalan (ca) Desigualtat de Sobolev		2

More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

Language versions of the article "Sobolev inequality" with the highest AI in June 2025

#	Language	AI award	Relative AI
1	Catalan (ca) Desigualtat de Sobolev		0
2	English (en) Sobolev inequality		0
3	French (fr) Injections de Sobolev		0
4	Italian (it) Disuguaglianza di Sobolev		0
5	Japanese (ja) ソボレフ不等式		0
6	Chinese (zh) 索博列夫不等式		0

More...

The following table shows the language versions of the article with the highest number of citations.

Language versions of the article "Sobolev inequality" with the highest Citation Index (CI)

#	Language	CI award	Relative CI
1	English (en) Sobolev inequality		143
2	Italian (it) Disuguaglianza di Sobolev		22
3	Chinese (zh) 索博列夫不等式		17
4	Japanese (ja) ソボレフ不等式		16
5	French (fr) Injections de Sobolev		8
6	Catalan (ca) Desigualtat de Sobolev		1

More...

#	Language	Value
ca	Catalan Desigualtat de Sobolev
en	English Sobolev inequality
fr	French Injections de Sobolev
it	Italian Disuguaglianza di Sobolev
ja	Japanese ソボレフ不等式
zh	Chinese 索博列夫不等式

Best Rank

English: #200910 03.2015

Global: #313713 05.2025

Best Rank

English: #55863 07.2009

Global: #103856 05.2023

On 16 March 2026 in multilingual Wikipedia, Internet users most often read articles on the following topics: 98th Academy Awards, Michael B. Jordan, Sinners, Jessie Buckley, Paul Thomas Anderson, Sean Penn, One Battle After Another, Amy Madigan, Hamnet, Timothée Chalamet.

In English Wikipedia the most popular articles on that day were: 98th Academy Awards, Michael B. Jordan, Paul Thomas Anderson, Jessie Buckley, Sinners (2025 film), Amy Madigan, Autumn Durald Arkapaw, Maya Rudolph, Sean Penn, Academy Awards.

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information