Linked from

The 39 pages that link to Poisson's equation, each with the reason it gives.

• Partial differential equationBroader topic: It extends Laplace's equation to fields generated by distributed sources.

• Boundary value problemRelated: Its boundary value formulations model fields generated by sources within a domain.

• Green's functionBroader topic: Its Green's function computes potentials generated by charge or mass distributions.

• Gravitational potentialRelated: For Newtonian gravity, mass density determines potential through this equation.

• Electric potentialRelated: It determines electric potential from charge density in a region.

• Laplace's equationCompared with: It generalizes Laplace's equation by allowing sources within the domain.

• Newtonian gravityRelated: It relates the gravitational potential to the distribution of matter.

• Jeans instabilityRelated: It connects density perturbations to the gravitational field that drives their growth.

• Gravitational fieldRelated: It connects the spatial variation of gravitational potential to mass density.

• Elliptic partial differential equationBroader topic: It models elliptic fields generated by charges, masses, or other sources.

• LaplacianRelated: It uses the Laplacian to connect fields to their sources.

• Weak solutionBroader topic: Its integral formulation produces a standard model for weak solutions and energy methods.

• Dirichlet boundary conditionRelated: Its solutions also use prescribed boundary values alongside an interior source.

• Gauss's lawCompared with: In electrostatics it determines potential from charge density, complementing Gauss's field equation.

• Potential theoryRelated: It models potentials produced by distributed sources rather than source-free regions.

• Neumann boundary conditionRelated: Neumann data prescribe boundary flux when solving this equation, subject to a compatibility condition.

• Depletion regionRelated: Applied to fixed dopant charge, it determines the field and potential profile.

• Helmholtz equationCompared with: It is the zero-frequency limit of the inhomogeneous Helmholtz equation.

• Fredholm alternativeBroader topic: Boundary conditions can produce a linear operator equation whose compatibility is tested by the alternative.

• Fundamental solutionRelated: Its fundamental solution gives the potential produced by a point source.

• Stellar dynamicsRelated: It determines how stellar mass density generates the gravitational potential.

• Elliptic regularityBroader topic: Its solutions gain derivatives according to the regularity of the source and boundary data.

• Conjugate gradient methodBroader topic: Discretizing this equation yields a standard test case for conjugate-gradient solvers.

• Siméon Denis PoissonBroader topic: Poisson formulated this equation, central to potential theory and mathematical physics.

• Elliptic operatorBroader topic: It is a central inhomogeneous elliptic equation in physics and mathematics.

• Lax–Milgram theoremBroader topic: Its Dirichlet problem is a standard example whose weak solution follows from the theorem.

• Nernst–Planck equationRelated: Coupling it to ionic concentrations determines the electric field driving migration.

• Earnshaw's theoremRelated: It generalizes the charge-free equation that supplies Earnshaw’s key constraint.

• Douglas HartreeRelated: Hartree’s electrostatic potential can be computed from electron density using this equation.

• Jeans equationsRelated: Together, it and the Jeans equations can constrain a system’s mass distribution.

• Successive over-relaxationBroader topic: Finite-difference Poisson problems produce systems often solved with SOR.

• Vlasov equationRelated: In electrostatic and gravitational models, it closes the Vlasov system by deriving fields from particle density.

• EquipotentialRelated: It determines potential curvature where charge or mass sources are present.

• Fredholm's theoremRelated: Boundary-constrained Poisson problems illustrate existence conditions and non-uniqueness from null spaces.

• Friedrichs' inequalityRelated: With suitable boundary data, the inequality controls solution norms through their gradients.

• Gauss's law for gravityRelated: It is the differential form of the gravitational flux law.

• Lions–Lax–Milgram theoremBroader topic: Its weak Dirichlet formulation is a standard coercive application.

• Vlasov–Fokker–Planck modelRelated: It often determines the self-consistent electrostatic potential from the particle density.

• Weyl's lemmaCompared with: Unlike Weyl's homogeneous hypothesis, a nonzero source generally prevents the conclusion of harmonicity.