estimates on the critical and singular sets $$\begin{aligned}
&{\mathcal{C}}(u)\equiv\{x\in B_{1/2}(0):|\nabla u|=0\}\, ,\,\,\,\,\, {\mathcal{S}}(u)\equiv\{x\in B_{1/2}(0):u=|\nabla u|=0\}\, .\end{aligned}$$ In principal, for general equations we will prove estimates on ${\mathcal{S}}(u)$, while for critical equations we will prove estimates on ${\mathcal{C}}(u)$. It will be convenient to denote by ${\mathcal{CS}}(u)$ either the critical set ${\mathcal{C}}(u)$ or singular set ${\mathcal{S}}(u)$, depending on whether the equation (\[eq\_Lu\]) is critical or not, respectively. Note that if we wish to control the $n-2$-measure of critical or singular sets, then the assumption of Lipschitz coefficients is a sharp assumption, since if the coefficients are only Hölder one can find nontrivial solutions which vanish on open subsets, see [@plis].\
More importantly we will prove estimates on the [*effective*]{} critical and singular sets ${\mathcal{C}}_r(u)$, ${\mathcal{S}}_r(u)$. The effective critical and singular sets were first introduced by the authors in [@chnava]. In essence, $x\in {\mathcal{C}}_r(u)$ if on the definite size ball $B_r(x)$ we have that $|\nabla u|$ has a definite size relative to $u$, more precisely we have:

$$\begin{aligned}
\label{e:effective_critical}
&{\mathcal{C}}_r(u)\equiv{\left\{x\in B_{1/2}(0): \inf_{B_r(x)}|\nabla u|^2 < \frac{n}{16r^2}\fint_{\partial B_{2r}(x)} |u-u(x)|^2\right\}}\, ,\notag\\
&{\mathcal{S}}_r(u)\equiv{\left\{x\in B_{1/2}(0): \inf_{B_r(x)}{\left({\left|u\right|}^2 + \frac{r^2}{n} |\nabla u|^2 \right)} < \frac{1}{16}\fint_{\partial B_{2r}(x)} |u|^2\right\}}\, .\end{aligned}$$

Again we will denote by ${\mathcal{CS}}_r(u)$ the effective critical or singular set, 