3 problems

Let a cuboid be a Euclidean rectangular box, and let two cuboids be Steklov isospectral when their Steklov spectra, counted with multiplicities, coincide. Steklov spectral determin…

Let $0\leq a\leq b\leq c=1$, and let $\sigma_1$ denote the first Steklov eigenvalue of the cuboid. Define $\lambda_1$ and $\lambda_2$ as the parameters occurring in the separated e…

Let the cuboid be $[-a,a]\times[-b,b]\times[-1,1]$, with $a,b\leq 1$, and consider the surface plotting its first Steklov invariant in the first octant. Differentiability and origi…