椭圆型偏微分方程（英语：Elliptic partial differential equation）是一类二阶偏微分方程，形式为：

并满足

(另有隐含条件 . )

Second order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second order linear PDE in two variables can be written in the form

where A, B, C, D, E, F, and G are functions of x and y. A PDE written in this form is elliptic if