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...

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

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

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

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...

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

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

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...

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

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

In mathematics, k-Hessian equations (or Hessian equations for short) are partial differential equations (PDEs) based on the Hessian matrix. More specifically...

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

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

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

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

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

The omega equation is a culminating result in synoptic-scale meteorology. It is an elliptic partial differential equation, named because its left-hand...

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

In mathematics, the biharmonic equation is a fourth-order partial differential equation which arises in areas of continuum mechanics, including linear...

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

method of lines (MOL, NMOL, NUMOL) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized. By reducing...

differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator...

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...

theory of partial differential equations and quantum field theory, e.g. in mathematical models that include ultrametric pseudo-differential equations in a...