Phuong Le

Rigidity and symmetry breaking in a Serrin problem with a radial variable exponent

We study Serrin's overdetermined torsion problem for the $p(|x|)$-Laplacian in bounded domains containing the origin. An explicit radial solution has flux $-x/n$ and gradient modulus $f(r)=(r/n)^{1/(p(r)-1)}$. Comparison with this solution yields two-sided boundary-gradient bound...