ASYMPTOTICS OF EIGENVALUES FOR THE
LAPLACE EQUATION IN DOMAINS WITH SLOTS

I. M. Martynenko

UDC 517.9:539.3

The asymptotic formula for the eigenvalues of the Laplace 
equation in three-dimensional domains bounded by a finite number of 
closed and open nonintersecting Lyapunov surfaces with smooth boundaries 
has been derived. This result is of importance in calculating stationary 
thermal conductivity in solid bodies in the presence of slots in them.

Belarusian State University, 4 Nezavisimost' Ave., Minsk, 220050, Belarus. 
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 3, pp. 577-582, 
May-June, 2008. Original article submitted September 4, 2006.