mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are frequently...

A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent...

In mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking...

mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The...

In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined...

of partial differential equation topics. Partial differential equation Nonlinear partial differential equation list of nonlinear partial differential equations...

the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation: ∇ 2 f = − k 2...

In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its...

principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. In this method, functions are represented by their...

between invariants of an ellipse A differential equation with an elliptic operator An elliptic partial differential equation This disambiguation page lists...

(real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function...

which case the HJB equation is a second-order elliptic partial differential equation. A major drawback, however, is that the HJB equation admits classical...

EFE are a system of ten coupled, nonlinear, hyperbolic-elliptic partial differential equations. The above form of the EFE is the standard established...

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

Electrostatic Analogs Gilbarg, D.; Trudinger, N. (2001), Elliptic Partial Differential Equations of Second Order, Springer, ISBN 978-3-540-41160-4. Schey...

result in the analysis of elliptic partial differential equations. In the present context, the relevant elliptic equation is the condition for a function...

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

work, principally an analysis of an elliptic partial differential equation known as the complex Monge–Ampère equation, was an influential early result in...

mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability...

specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier...

equation takes the same form as the Hicks equation from fluid dynamics. This equation is a two-dimensional, nonlinear, elliptic partial differential equation...

precisely as a variational problem whose Euler–Lagrange equation is an elliptic partial differential equation with analytic coefficients, Hilbert's nineteenth...

discretizing integral equations, preconditioning the resulting systems of linear equations, or solving elliptic partial differential equations, a rank proportional...

In the mathematical field of differential equations, the ultrahyperbolic equation is a partial differential equation (PDE) for an unknown scalar function...

boundary value problems known as linear elliptic problems. Boundary value problems and partial differential equations specify relations between two or more...

Liouville's equation, named after Joseph Liouville, is the nonlinear partial differential equation satisfied by the conformal factor f of a metric f2(dx2 + dy2)...

with the theory of elliptic equations, will enable us to organize the solutions of this equation. A concrete example would be an elliptic boundary-value problem...

periodic motion, or in the analysis of partial differential equation (PDE) boundary value problems possessing elliptic symmetry. In some usages, Mathieu function...

In the theory of partial differential equations, a partial differential operator P {\displaystyle P} defined on an open subset U ⊂ R n {\displaystyle U\subset...

generalized Harnack's inequality to solutions of elliptic or parabolic partial differential equations. Such results can be used to show the interior regularity...