Dirichlet's energy

half of the integral of the squared gradient of a function on its domain
Thing unit_of_measurement Q5280760
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Dirichlet's energy

Summary

Dirichlet's energy is an unit of measurement[1]. It draws 43 Wikipedia views per month (unit_of_measurement category, ranking #43 of 115).[2]

Key Facts

  • Dirichlet's energy's instance of is recorded as unit of measurement[3].
  • Johann Peter Gustav Lejeune Dirichlet is named after Dirichlet's energy[4].
  • Dirichlet's energy's Freebase ID is recorded as /m/03d207y[5].
  • Dirichlet's energy's defining formula is recorded as E[u]=\frac12\int_\Omega \left|\nabla u(x)\right|^2\,\mathrm dx[6].
  • Dirichlet's energy's MathWorld ID is recorded as DirichletEnergy[7].
  • Dirichlet's energy's maintained by WikiProject is recorded as WikiProject Mathematics[8].
  • Dirichlet's energy's Microsoft Academic ID is recorded as 96234433[9].
  • Dirichlet's energy's in defining formula is recorded as E[10].
  • Dirichlet's energy's in defining formula is recorded as \Omega[11].
  • Dirichlet's energy's in defining formula is recorded as \nabla[12].
  • Dirichlet's energy's in defining formula is recorded as u[13].
  • Dirichlet's energy's in defining formula is recorded as \left|~\right|[14].
  • Dirichlet's energy's in defining formula is recorded as ^2[15].
  • Dirichlet's energy's in defining formula is recorded as \frac12[16].
  • Dirichlet's energy's OpenAlex ID is recorded as C96234433[17].

Why It Matters

Dirichlet's energy draws 43 Wikipedia views per month (unit_of_measurement category, ranking #43 of 115).[2] It has Wikipedia articles in 7 language editions, a strong signal of global cultural recognition.[18] It is known by 3 alternative names across languages and contexts.[19]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [18] . Wikidata sitelinks. wikidata.org.
  3. [19] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Dirichlet's energy. Retrieved May 3, 2026, from https://4ort.xyz/entity/dirichlet-s-energy
MLA “Dirichlet's energy.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/dirichlet-s-energy.
BibTeX @misc{4ortxyz_dirichlet-s-energy_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Dirichlet's energy}}, year = {2026}, url = {https://4ort.xyz/entity/dirichlet-s-energy}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Dirichlet's energy — https://4ort.xyz/entity/dirichlet-s-energy (retrieved 2026-05-03)

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