Variational formula and overdetermined problem for the principal eigenvalue of \(k\)-Hessian operator (Q2637797)

The authors study the principal (first) eigenvalue \(\lambda_1^k(\Omega)\) of the \(k\)-Hessian operator on a \((k-1)\)-convex domain \(\Omega\). The main results are the first variational formula and some overdetermined problems for \(\lambda_1^k(\Omega)\). For the latter ones, the authors also provide some Serrin type symmetry results.