Brezis' radial symmetry conjecture for boundary blow-up solutions

Let $f\in C^1(\mathbb R)$ satisfy the positivity and Keller–Osserman conditions, and let $u$ be a solution of the boundary blow-up problem studied in the source on the unit ball $B\subset\mathbb R^N$. A radially symmetric solution depends only on $|x|$. Brezis' radial symmetry conjecture. Every such solution $u$ is radially symmetric. This conjecture concerns whether boundary blow-up solutions in the unit ball must inherit the ball's rotational symmetry. The source attributes it to H. Brezis and supplies no resolution.