On the lack of directional quasiconcavity of the fundamental mode in the clamped membrane problem
It is well known that the first eigenfunction of the Laplacian in a bounded convex region under Dirichlet boundary condition has convex level sets. In 1994 the reviewer asked if a corresponding statement holds if the domain is merely convex in one direction [in: Partial differential equations of elliptic type. Cambridge: University Press. Symp. Math. 35, 165--183 (1994; Zbl 0827.35083)]. In this note the author provides a negative answer in the form of a well designed two-dimensional counterexample.
scientific article; zbMATH DE number 5988054