The uniqueness theorem for Poisson's equation states that, for a large class of boundary conditions, the equation may have many solutions, but the gradient...

Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation...

differential equations. Thompson uniqueness theorem in finite group theory. Uniqueness theorem for Poisson's equation. Electromagnetism uniqueness theorem for the...

charges Uniqueness theorem for Poisson's equation List of examples of Stigler's law The other three of Maxwell's equations are: Gauss's law for magnetism...

\Delta f=h} This is called Poisson's equation, a generalization of Laplace's equation. Laplace's equation and Poisson's equation are the simplest examples...

choice varies from PDE to PDE. To understand it for any given equation, existence and uniqueness theorems are usually important organizational principles...

Poisson's equation—or in the vacuum, Laplace's equation. There is considerable overlap between potential theory and the theory of Poisson's equation to...

that the boundary conditions are satisfied, then by the uniqueness theorem for Poisson's equation, we must have found the solution. The continuity conditions...

{\displaystyle a(u,v)=\mathbf {v} ^{T}\mathbf {A} \mathbf {u} .} To solve Poisson's equation − ∇ 2 u = f , {\displaystyle -\nabla ^{2}u=f,} on a domain Ω ⊂ R d...

innovations. Many of these items named after Euler include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical...

Campbell's theorem (probability) Compound Poisson process Continuous-time Markov process Little's lemma Lotka's integral equation Palm–Khintchine theorem Poisson...

velocity together with an elliptic Poisson's equation for the pressure. On the other hand, the compressible Euler equations form a quasilinear hyperbolic system...

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form...

of Poisson's work, and the result was not well known during his time. Over the following years others used the distribution without citing Poisson, including...

Coulomb's law Divergence theorem Flux Gaussian surface Schwarz reflection principle Uniqueness theorem for Poisson's equation Image antenna Surface equivalence...

in the configuration space be fixed. The existence and uniqueness theorems guarantee that, for every v 0 , {\displaystyle \mathbf {v} _{0},} the initial...

Milgram theorem by Peter Lax and Arthur Milgram. In the modern, functional-analytic approach to the study of partial differential equations, one does...

the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose...

mathematical model for the number of incoming phone calls in a finite time interval. Erlang was not at the time aware of Poisson's earlier work and assumed...

Helmholtz theorem (also known as the fundamental theorem of vector calculus). The first equation is a pressureless governing equation for the velocity...

Tzitzeica equation Rabinovich–Fabrikant equations General Legendre equation Heat equation Laplace's equation in potential theory Poisson's equation in potential...

the rules for evaluating a Poisson bracket without resorting to differential equations, see Lie algebra; a Poisson bracket is the name for the Lie bracket...

In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest...

part of Noether's theorem, we find the implicit variation in the Lagrangian due to variation of fields. If the equation of motion for ψ , ψ ¯ {\displaystyle...

approach in several ways. E.g., first-order FEM is identical to FDM for Poisson's equation if the problem is discretized by a regular rectangular mesh with...

voltages. By Gauss's law, the potential can also be found to satisfy Poisson's equation: ∇ ⋅ E = ∇ ⋅ ( − ∇ V E ) = − ∇ 2 V E = ρ / ε 0 {\displaystyle \mathbf...

formula for the Newtonian potential (the fundamental solution of Poisson's equation). This is essentially a form of the inversion formula for the Radon...

Using this expression, it is possible to solve Laplace's equation ∇2φ(x) = 0 or Poisson's equation ∇2φ(x) = −ρ(x), subject to either Neumann or Dirichlet...

The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves...

eigenvalue of Laplace's equation on general domains towards the end of the 19th century, while Poincaré studied Poisson's equation a few years later. At...