Elliptic operators are a class of differential operators that arise in the study of partial differential equations (PDEs). They are characterized by their ability to ensure the existence and uniqueness of solutions under certain conditions. A common example is the Laplace operator, which is used in various fields such as physics and engineering to model phenomena like heat conduction and fluid flow. These operators are defined on smooth functions and are typically associated with elliptic equations, which are a type of PDE. The properties of elliptic operators make them essential in functional analysis and geometry, as they help in understanding the behavior of solutions and their regularity.