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Dirichlet's problem

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  • 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 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 eta function — For the modular form see Dedekind eta function. Dirichlet eta function η(s) in the complex plane. The color of a point s encodes the value of η(s). Strong colors denote values close to zero and hue encodes the value s argumen …   Wikipedia

  • Dirichlet , (Peter Gustav) Lejeune — (1805–1859) German mathematician Born in Düren (now in Germany), Dirichlet studied mathematics at Göttingen where he was a pupil of Karl Gauss and Karl Jacobi. He also studied briefly in Paris where he met Joseph Fourier, who stimulated his… …   Scientists

  • 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 problem — ▪ mathematics       in mathematics, the problem of formulating and solving certain partial differential equations (partial differential equation) that arise in studies of the flow of heat, electricity, and fluids. Initially, the problem was to… …   Universalium

  • Dirichlet-Randbedingung — Als Dirichlet Randbedingung (nach Peter Gustav Lejeune Dirichlet) bezeichnet man im Zusammenhang mit Differentialgleichungen (genauer: Randwertproblemen) Werte, die auf dem jeweiligen Rand des Definitionsbereichs von der Funktion angenommen… …   Deutsch Wikipedia

  • Dirichlet's theorem on arithmetic progressions — In number theory, Dirichlet s theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n ≥ 0. In other… …   Wikipedia

  • Dirichlet density — This article is not about the Dirichlet distribution of probability theory. In mathematics, the Dirichlet density (or analytic density) of a set of primes, named after Johann Gustav Dirichlet, is a measure of the size of the set that is easier to …   Wikipedia

  • Dirichlet-Problem — Als Dirichlet Randbedingung (nach Peter Gustav Lejeune Dirichlet) bezeichnet man im Zusammenhang mit Differentialgleichungen (genauer: Randwertproblemen), Werte, die auf dem jeweiligen Rand des Definitionsbereichs von der Funktion angenommen… …   Deutsch 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

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