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Dirichlet energy

Dirichlet energy noun: a quadratic functional which, given a real function defined on an open subset of ℝⁿ, yields a real number that is a measure of how variable said function is.

Noun

Dirichlet energy (plural Dirichlet energies)

  1. (functional analysis, Fourier analysis) A quadratic functional which, given a real function defined on an open subset of ℝⁿ, yields a real number that is a measure of how variable said function is.
    • Variational principles play an important role in both geometry and physics, and one of the key problems with applications in both fields is the variational problem associated to the Dirichlet energy of maps between Riemannian manifolds.2005, Roger Moser, Partial Regularity for Harmonic Maps and Related Problems, World Scientific, page 1
    • The Dirichlet energy of a function f#92;inW#123;1,2#125; can be recovered, moreover, as the energy of the composition #92;xi#95;#123;BW#125;#92;circf, where #92;xi#95;#123;BW#125; is the biLipschitz embedding in Corollary 2.2 (compare with Theorem 2.4).2011, Camillo De Lellis, Emanuele Nunzio Spadaro, Q-valued Functions Revisited, American Mathematical Society, page 28

Forms of Dirichlet energy

pluralDirichlet energies
alternative formDirichlet's energy

Origin of Dirichlet energy

Named after German mathematician Peter Gustav Lejeune Dirichlet (1805–1859), who made significant contributions to the theory of Fourier series.

Questions about Dirichlet energy

What does Dirichlet energy mean?
Dirichlet energy means a quadratic functional which, given a real function defined on an open subset of ℝⁿ, yields a real number that is a measure of how variable said function is.
What part of speech is Dirichlet energy?
Dirichlet energy is a noun.
What is the plural of Dirichlet energy?
The plural of Dirichlet energy is Dirichlet energies.

Words near Dirichlet energy in the dictionary

  1. Dirichlet character
  2. Dirichlet characters
  3. Dirichlet distribution
  4. Dirichlet distributions
  5. Dirichlet energies
  6. Dirichlet energy
  7. Dirichlet eta function
  8. Dirichlet problem
  9. Dirichlet problems
  10. Dirichlet process
  11. Dirichlet processes

Source and license

Adapted from Wiktionary: Dirichlet energy (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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