Applications to Partial Differential Equations

Abstract

Recall from Chapter 2 that the differential operator L of order p in n independent variables x ₁,x ₂, …,x _n ,is

$$ Lu = \sum\limits_{\left| k \right| \leqslant p} {a_k (x)D^k u,} $$

(1)

where the coefficients a _k have partial derivatives of all orders. Its formal adjoint L* is defined as

$$ L*v = \sum\limits_{\left| k \right| \leqslant p} {( - 1)^k D^k (a_k v).} $$

(2)