Eigenfunctions of Laplacians in some two-dimensional domains
Ya. G. Sinaǐ, I. Vinogradov · Contemporary mathematics - American Mathematical Society · 2017
We construct eigenfunctions of a modified Laplace operator in certain two-dimensional polygonal domains with Dirichlet boundary condition. A special property of domains is the existence of a lattice on which our operator can be defined. This allows us to give explicit expressions for eigenfunctions.