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...

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

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

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

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...

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

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...

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

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

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

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

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

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

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

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

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...

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

The Navier–Stokes equations (/nævˈjeɪ stoʊks/ nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances...

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

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...

(1998), Partial Differential Equations, American Mathematical Society. Gilbarg, David; Trudinger, Neil (12 January 2001), Elliptic Partial Differential Equations...

parabolic partial differential equations, zeros of the principal symbol correspond to the characteristics of the partial differential equation. In applications...

where tools from differential equations, especially elliptic partial differential equations are used to establish new results in differential geometry and...

Elliptic coordinates, an orthogonal coordinate system based on families of ellipses and hyperbolae Elliptic partial differential equation Elliptical distribution...