Glasnik Matematicki, Vol. 33, No.1 (1998), 61-69.

ON A GENERAL ASYMPTOTIC PROBLEM ASSOCIATED WITH LERAY-LIONS OPERATORS

Mervan Pašić

Abstract.   Firstly, we prove a pointwise comparison result for the suitable symmetrized problem that depends ona small positive parameter λ. Then, by these results and by thze Schwarz symmetrization, we obtain some asymtotic relationship between the solutions u_ε of a general ε and a sequence of real numbers λ_ε. Finally, it is shown an application of the preceding results to getting a priori estimates in the homogenization theory.

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.