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Dirichlet principle

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  • Dirichlet integral — In mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet. One of those is This can be derived from attempts to evaluate a double improper integral two different… …   Wikipedia

  • Dirichlet's theorem — may refer to any of several mathematical theorems due to Johann Peter Gustav Lejeune Dirichlet. Dirichlet s theorem on arithmetic progressions Dirichlet s approximation theorem Dirichlet s unit theorem Dirichlet conditions Dirichlet boundary… …   Wikipedia

  • Dirichlet's principle — Not to be confused with Pigeonhole principle. In mathematics, Dirichlet s principle in potential theory states that, if the function u(x) is the solution to Poisson s equation on a domain Ω of with boundary condition then u can be obtained as the …   Wikipedia

  • Dirichlet problem — In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region. The Dirichlet… …   Wikipedia

  • Dirichlet's approximation theorem — In number theory, Dirichlet s theorem on Diophantine approximation, also called Dirichlet s approximation theorem, states that for any real number α and any positive integer N, there exists integers p and q such that 1 ≤ q ≤ N and This is a… …   Wikipedia

  • Dirichlet eigenvalue — In mathematics, the Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. The problem of whether one can hear the shape of a drum is: given the Dirichlet eigenvalues, what features of the shape of… …   Wikipedia

  • Dirichlet-Prinzip — Das Dirichlet Prinzip in der Potentialtheorie besagt, dass Funktionen u in einem Gebiet (mit vorgegebenen Werten u = g auf dem Rand von G), die das „Energiefunktional“ (Dirichlet Integral) mini …   Deutsch Wikipedia

  • Dirichlet form — In mathematics, a Dirichlet form is a Markovian closed symmetric form on an L2 space.[1] Such objects are studied in abstract potential theory, based on the classical Dirichlet s principle. The theory of Dirichlet forms originated in the work of… …   Wikipedia

  • Dirichlet kernel — In mathematical analysis, the Dirichlet kernel is the collection of functions It is named after Johann Peter Gustav Lejeune Dirichlet. The importance of the Dirichlet kernel comes from its relation to Fourier series. The convolution of Dn(x) with …   Wikipedia

  • Dirichlet's unit theorem — In mathematics, Dirichlet s unit theorem is a basic result in algebraic number theory due to Gustav Lejeune Dirichlet.[1] It determines the rank of the group of units in the ring OK of algebraic integers of a number field K. The regulator is a… …   Wikipedia

  • Dirichlet's energy — In mathematics, the Dirichlet s energy is a numerical measure of how variable a function is. More abstractly, it is a quadratic functional on the Sobolev space H1. The Dirichlet energy is intimately connected to Laplace s equation and is named… …   Wikipedia

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