Elliptic partial differential equation

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In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are frequently used to model steady states, unlike parabolic and hyperbolic PDEs, which generally model phenomena that change in time. The canonical examples of elliptic PDEs are Laplace's equation and Poisson's equation. Elliptic PDEs are also important in pure mathematics, where they are fundamental to various fields of research such as differential geometry and optimal transport.

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