The elliptic PDE −Δu = f on Ω (plus boundary data). Classical solvability via Green's functions; variational formulation via minimising ½∫|∇u|² − ∫fu in H¹₀.
Poisson equation
Related concepts
- Laplace equation
- Green's function
- Multigrid method
- Poisson kernel P_r(θ) reconstructs harmonic u from ∂D data
- Grad-Shafranov Δ*ψ = -μ₀R²P'(ψ) - FF'(ψ); Soloviev analytic equilibrium
- NFW dark-matter halo profile
- Gouy-Chapman diffuse-layer framework: κ^(−1) = sqrt(ε·ε₀·R·T/(2·F²·I)) (Debye length ∝ I^(−1/2))
- Hydration enthalpy — Born model
- Born model of ion solvation