Introduction: What Are Partial Differential Equations?

Abstract

As a first answer to the question, What are partial differential equations, we would like to give a definition: Definition 1: A partial differential equation (PDE) is an equation involving derivatives of an unknown function u: Ω → ℝ, where Ω is an open subset of ℝ^d, d ≥ 2 (or, more generally, of a differentiable manifold of dimension d ≥ 2).