Extend level-set results to higher-order and nonlinear operators

Establish whether analogues of the geometric and stability results for level sets proved in the paper extend to higher-order or nonlinear operators, including the p-Laplacian and related operators.

Background

The paper develops a comprehensive geometric theory for level sets associated with linear second-order problems and a coupled biharmonic system, proving star-shapedness, curvature identities, asymptotics near contact points, and stability under Hausdorff convergence.

The authors explicitly raise the question of whether these methods and conclusions carry over to more general operators, notably the p-Laplacian and other higher-order PDEs.