Interior regularity of some weighted quasi-linear equations

In this article we study the quasi-linear equation $$\{\begin{array}{rlrl}{\displaystyle \mathrm{d}\mathrm{i}\mathrm{v}\mathcal{A}(x,u,\mathrm{\nabla }u)}& {\displaystyle =\mathcal{B}(x,u,\mathrm{\nabla }u)}& {\displaystyle }& {\displaystyle \text{in }\mathrm{\Omega },}\\ {\displaystyle u\in H_{loc}^{1,p}}& {\displaystyle (\mathrm{\Omega };wdx)}\end{array}$$ where $\mathcal{A}$ and $\mathcal{B}$ are functions satisfying $\mathcal{A}(x,u,\mathrm{\nabla }u)\sim \mathcal{B}(x,u,\mathrm{\nabla }u)\sim w(\mathrm{\mid }\mathrm{\nabla }u{\mathrm{\mid }}^{p-2}\mathrm{\nabla }u+\mathrm{\mid }u{\mathrm{\mid }}^{p-2}u)$ for $p>1$ and a $p$-admissible weight function $w$. We establish interior regularity results of weak solutions and use those results to obtain point-wise asymptotic estimates for solutions to $$\{\begin{array}{rlrl}{\displaystyle -\mathrm{d}\mathrm{i}\mathrm{v}(w\mathrm{\mid }\mathrm{\nabla }u{\mathrm{\mid }}^{p-2}\mathrm{\nabla }u)}& {\displaystyle =w\mathrm{\mid }u{\mathrm{\mid }}^{q-2}u}& {\displaystyle }& {\displaystyle \text{in }\mathrm{\Omega },}\\ {\displaystyle u\in D^{1,p}}& {\displaystyle (\mathrm{\Omega },wdx)}\end{array}$$ for a critical exponent $q>p$ in the sense of Sobolev.