Liouville type theorems and regularity of solutions to degenerate or singular problems part II: odd solutions

We consider a class of equations in divergence form with singular/degenerate weight $$ -\mathrm{div}(|y|^a A(x,y)\nabla u)=|y|^a f(x,y)+\textrm{div}(|y|^aF(x,y))\;. Under suitable regularity assumptions for the matrix $A$, forcing term $f$ and field $F$, we prove H\"older continuity solutions which are odd $y\in\mathbb{R}$, possibly their derivatives. In addition, show stability $C^{0,\alpha}$ $C^{1,\alpha}$ priori bounds approximating problems -\mathrm{div}((\varepsilon^2+y^2)^{a/2} u)=(\varepsilon^2+y^2)^{a/2} f(x,y)+\textrm{div}((\varepsilon^2+y^2)^{a/2}F(x,y)) as $\varepsilon\to 0$. Our method is based upon blow-up appropriate Liouville type theorems.