A Sanchez-Palencia problem with Neumann boundary conditions. (English. Russian original) Zbl 0801.35092

Sov. Math. 33, No. 11, 73-78 (1989); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1989, No. 11(330), 60-66 (1989).
In a previous paper, Sanchez-Palencia considered a perturbed spectral Dirichlet problem – a mathematical model in the frame of thermoelasticity and vibration of systems with concentrated masses [E. Sanchez-Palencia, Lect. Notes Phys. 195, 346-368 (1984; Zbl 0542.73006)]. The author considers a perturbed spectral Neumann problem and studies the asymptotic behaviour of its eigenvalues and eigenfunctions when the parameter tends to zero. The method employed for this study is the same as that used previously for the study of Sanchez- Palencia’s problem.


35P05 General topics in linear spectral theory for PDEs
35J25 Boundary value problems for second-order elliptic equations


Zbl 0542.73006