Semilinear differential operator

This article defines a property that can be evaluated for a differential operator on a differential manifold (viz a linear map from the space of differentiable functions to itself)

Definition

A semilinear differential operator on a differential manifold $M$ is a map $C^{\mathrm{\infty }}(M)\to C^{\mathrm{\infty }}(M)$ that can be expressed as:

$f\mapsto Lf+g\circ f$

where $L$ is a linear differential operator and $g$ is an element of $C^{\mathrm{\infty }}(M)$.

Relation with other properties

Stronger properties

• Linear differential operator

Weaker properties

• Quasilinear differential operator

External links

• Template:Dispersivewiki