De Giorgi–Nash–Moser Theory

Abstract

We consider the second-order, linear, elliptic equations with divergence structure

$$\mathrm{div} (\mathbb{A}(x)\nabla u(x))\;=\;\sum\limits^n_{i,j=1}\;\partial_{x_{i}}(a_{ij}(x)\partial_{x_{j}}u(x))\;=\;0.$$