mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are frequently...
18 KB (2,591 words) - 12:14, 13 May 2025
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...
7 KB (1,149 words) - 16:53, 16 May 2025
In mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking...
9 KB (1,241 words) - 08:11, 21 October 2024
mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The...
49 KB (6,795 words) - 21:29, 14 May 2025
In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined...
13 KB (2,093 words) - 04:02, 18 April 2025
of partial differential equation topics. Partial differential equation Nonlinear partial differential equation list of nonlinear partial differential equations...
2 KB (157 words) - 18:19, 14 March 2022
the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation: ∇ 2 f = − k 2...
20 KB (2,975 words) - 18:26, 19 May 2025
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its...
33 KB (5,075 words) - 15:19, 13 April 2025
principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. In this method, functions are represented by their...
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between invariants of an ellipse A differential equation with an elliptic operator An elliptic partial differential equation This disambiguation page lists...
268 bytes (65 words) - 21:35, 2 September 2021
(real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function...
8 KB (1,011 words) - 23:49, 24 March 2023
which case the HJB equation is a second-order elliptic partial differential equation. A major drawback, however, is that the HJB equation admits classical...
14 KB (2,050 words) - 11:37, 3 May 2025
EFE are a system of ten coupled, nonlinear, hyperbolic-elliptic partial differential equations. The above form of the EFE is the standard established...
35 KB (5,077 words) - 15:22, 28 May 2025
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...
17 KB (2,371 words) - 13:58, 18 March 2025
Laplace operator (category Elliptic partial differential equations)
Electrostatic Analogs Gilbarg, D.; Trudinger, N. (2001), Elliptic Partial Differential Equations of Second Order, Springer, ISBN 978-3-540-41160-4. Schey...
30 KB (4,682 words) - 03:20, 8 May 2025
Isothermal coordinates (category Partial differential equations)
result in the analysis of elliptic partial differential equations. In the present context, the relevant elliptic equation is the condition for a function...
15 KB (1,918 words) - 19:15, 5 March 2024
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves...
60 KB (10,783 words) - 12:19, 24 May 2025
Calabi conjecture (redirect from Complex Monge-Ampère equation)
work, principally an analysis of an elliptic partial differential equation known as the complex Monge–Ampère equation, was an influential early result in...
11 KB (1,563 words) - 00:27, 13 June 2024
mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability...
42 KB (7,586 words) - 11:58, 24 May 2025
specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier...
58 KB (9,878 words) - 17:19, 28 May 2025
equation takes the same form as the Hicks equation from fluid dynamics. This equation is a two-dimensional, nonlinear, elliptic partial differential equation...
8 KB (1,469 words) - 09:04, 3 April 2025
Hilbert's nineteenth problem (category Partial differential equations)
precisely as a variational problem whose Euler–Lagrange equation is an elliptic partial differential equation with analytic coefficients, Hilbert's nineteenth...
28 KB (3,233 words) - 17:51, 25 May 2025
discretizing integral equations, preconditioning the resulting systems of linear equations, or solving elliptic partial differential equations, a rank proportional...
15 KB (2,149 words) - 21:04, 14 April 2025
In the mathematical field of differential equations, the ultrahyperbolic equation is a partial differential equation (PDE) for an unknown scalar function...
5 KB (568 words) - 07:36, 8 August 2023
boundary value problems known as linear elliptic problems. Boundary value problems and partial differential equations specify relations between two or more...
18 KB (3,615 words) - 14:17, 28 May 2025
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)...
8 KB (870 words) - 16:20, 10 May 2025
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...
10 KB (1,464 words) - 23:00, 25 November 2024
Mathieu function (redirect from Mathieu differential equation)
periodic motion, or in the analysis of partial differential equation (PDE) boundary value problems possessing elliptic symmetry. In some usages, Mathieu function...
44 KB (8,408 words) - 00:28, 26 May 2025
Hypoelliptic operator (redirect from Hypoelliptic partial differential equation)
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...
2 KB (314 words) - 08:13, 13 March 2025
generalized Harnack's inequality to solutions of elliptic or parabolic partial differential equations. Such results can be used to show the interior regularity...
8 KB (1,188 words) - 17:57, 19 May 2025