Interior regularity of doubly weighted quasi-linear equations
Interior regularity of doubly weighted quasi-linear equations
In this article we study the quasi-linear equation \[\mathrm{div}\, \mathcal A(x,u,\nabla u)=\mathcal B(x,u,\nabla u)\quad \text{in }\Omega,\qquad u\in H^{1,p}_{loc}(\Omega;w_1dx)\] where $\mathcal A$ and $\mathcal B$ are functions satisfying $\mathcal A(x,u,\nabla u)\sim w_1(|\nabla u|^{p-2}\nabla u+|u|^{p-2}u)$ and $\mathcal B(x,u,\nabla u)\sim w_2(|\nabla u|^{p-2}\nabla u+|u|^{p-2}u)$ for $p>1$, a $p$-admissible weight function $w_1$, and another weight …