Spectral Properties of the Laplace Operator with Variable Dependent Boundary Conditions in a Disk

Abstract

In this work, we study the spectral properties of the Laplace operator with variable dependent boundary conditions in a disk. The boundary conditions include periodic and antiperiodic boundary conditions as well as the generalized Samarskii–Ionkin-type boundary conditions. We show eigenfunctions and eigenvalues of these problems in an explicit form. Moreover, the completeness of their eigenfunctions is investigated.

Keywords

• Laplace operator
• Samarskii–Ionkin-type conditions
• completeness property
• eigenfunctions
• eigenvalues