Maximum principles for divergence structure elliptic differential inequalities

Abstract

For a large number of divergence structure equations, including equations which involve the important p-Laplacian operator Δp, there is a further series of maximum principles. In particular, in this chapter we study the differential inequality divA(x, u, Du) + B(x, u, Du) ≥ 0 in Ω, (3.1.1) where Ω is a bounded domain in ℝn (unless otherwise stated explicitly), and A(x, z, ξ): Ω × ℝ× ℝn → ℝn, B(x, z, ξ): Ω ×ℝ× ℝn → ℝ.