Abstract. Firstly, we prove a pointwise comparison result
for the suitable symmetrized problem that depends ona small positive
Then, by these results and by thze Schwarz symmetrization,
we obtain some asymtotic relationship between the solutions
1991 Mathematics Subject Classification. 35J15, 35B45.
Key words and phrases. Pointwise comparision problem with a parameter, Schwarz symmetrization, asymptotic problem, an application to the homogenization theory.