ABSTRACT
Given a domain Ω in the n-dimensional Euclidean space consisting of points x 1, x 2,..., x n , the following functional representation F ( x 1 , x 2 , . . . , x n ; ϕ ; ϕ x 1 , ϕ x 2 , . . . , ϕ x n ; ϕ x 1 x 1 , ϕ x 1 x 2 , . . . . ϕ x 1 x n , . . . , ) = 0 , x 1 , x 2 , . . . , x n ( ≡ x ) ∈ Ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429276477/5e6b97b3-f700-4dc6-82d7-7fdf47b0f880/content/math2_1.jpg"/> furnishes a PDE with respect to an unknown function ϕ(x). The order of the highest derivative occurring in (2.1) determines the order of the PDE.
