set. Unfortunately, while such an estimate is much stronger than $\dim{\mathcal{CS}}(u) = n-2$, the existence of the $\epsilon$ still prevents one from obtaining finiteness of the $n-2$-measure.

Main Results
------------

Now we briefly describe our main new results.

#### Main Result for Critical and Singular Sets:

In this paper we have developed a new method for controlling the critical and singular sets, distinct from the techniques of either [@chnava] or [@hanlin]. Before discussing the methods, let us state our main results and compare them to the literature:

\[t:main\_critical\] Let $u:B_1(0)\to {\mathds{R}}$ solve (\[eq\_Lu\]) with lipschitz coefficients satisfying (\[e:coefficient\_estimates\]). There exists $r_0=r_0(n,\lambda)>0$ and $C=C(n,\lambda)$ such that if $\Lambda\equiv N^u(0,2r_0)$, then the following Minkowski estimates hold: $$\begin{aligned}
\label{e:mink_est}
{\operatorname{Vol}}(B_r({\mathcal{CS}}(u))\cap B_{r_0}(0)) \leq {\operatorname{Vol}}(B_r({\mathcal{CS}}_r(u))\cap B_{r_0}(0)) \leq C^{\Lambda^2}\, r^2\, .\end{aligned}$$ In particular, we have the much weaker estimate on the Hausdorff measure $$\begin{aligned}
\label{e:haus_est}
{\mathcal{H}}^{n-2}({\mathcal{CS}}(u)\cap B_{r_0}(0))\leq C^{\Lambda^2}\, .\end{aligned}$$

Since this statement is scale invariant, we will assume for convenience that $r_0\geq 1$. This can be obtained using a suitable blow-up of the domain of the function $u$, or, equivalently, by assuming $\lambda$ to be small enough.

Before continuing let us make some remarks about Theorem \[t:main\_critical\]. Even under the assumption of analytic coefficients the Hausdorff 