elliptictype
Elliptic type refers to a class of partial differential equations and differential operators characterized by a positive definite principal part. The designation is part of the standard elliptic–hyperbolic–parabolic classification used for second-order PDEs, and signals equations whose solutions tend to be smooth and governed by boundary-value problems.
For a second-order linear PDE in variables x = (x1, ..., xn), an operator of the form sum
Common elliptic equations include the Laplace equation Δu = 0 and the Poisson equation Δu = f, the
Applications span physics, geometry, engineering, and image processing. In geometry and analysis, elliptic operators on manifolds
The term is often contrasted with hyperbolic and parabolic types, which model wave-like and diffusion-like phenomena,