Symmetry and nonuniformly elliptic operators. (Q976584)

The \(p\)-Laplacian problem \(\Delta _pu+f(u)=0\) \((p>2)\) with the Dirichlet condition on a ball in \(\mathbb R^d\) \((d\geq 1)\) and \(f\) continuous is considered. Local and global symmetry results for solutions \(u\in C^{1,\gamma }\) for \(\gamma \) large enough are proved under some additional assumptions.