Uniformly Elliptic Equations in Nondivergence Form

Abstract

In this chapter we consider linear operators of the form Lu=∑i,j=1naij(x)Diju(x)$$\displaystyle{Lu =\sum _{ i,j=1}^{n}a_{ ij}(x)D_{ij}u(x)}$$ where the coefficient matrix A(x) = (aij(x)) is symmetric and uniformly elliptic, that is λ|ξ|2≤⟨A(x)ξ,ξ⟩≤Λ|ξ|2,$$\displaystyle{\lambda \vert \xi \vert ^{2} \leq \langle A(x)\xi,\xi \rangle \leq \Lambda \vert \xi \vert ^{2},}$$ for all ξ∈ ℝ n and x∈ Ω ⊂ ℝ n.