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

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