Hölder continuity of solutions to an anisotropic elliptic equation (Q1030064)

The authors establish the Hölder continuity of solutions of \[ \sum\limits_{j=1}^{n-1}\partial_{x_j} a(x,u,\nabla u)+\partial_{x_n}^2 u+b(x,u,\nabla u)=0\qquad x\in\Omega \] on a domain \(\Omega\) of \({\mathbb R}^n\) assuming a degenerate ellipticity condition of the form \[ \sum\limits_{j=1}^{n-1} a(x,u,\xi)\xi_j\geq c_0 \sum\limits_{j=1}^{n-1} \left|\xi_j\right|^p- C \] and suitable growth conditions for \(a_j\) (\(j=1, \dots,n-1\)) and \(b\). Their proof relies on DiBenedetto's intrinsic rescaling method.