De Giorgi's continuity conjecture for singular elliptic equations

Let $\Omega\subset\mathbb{R}^N$ be a domain and consider weak solutions of

$$\operatorname{div}(A\nabla u)=0\quad\text{in }\Omega.$$

Assume that the coefficient matrix satisfies

$$|\xi|^2\leq A(x)\xi\cdot\xi\leq\Lambda(x)|\xi|^2$$

for $\xi\in\mathbb{R}^N$ and almost every $x\in\Omega$, with $N\geq3$ and $\lambda=1$. De Giorgi's continuity conjecture. If

$$\int_{\Omega}e^{\Lambda(x)}\,dx<\infty,$$

then every weak solution is continuous. This is one of De Giorgi's open problems for singular elliptic equations; the source states that the conjecture remains open.