Glasnik Matematicki, Vol. 41, No.1 (2006), 77-88.

A NOTE ON REDUCTION OF DIMENSION FOR LINEAR ELLIPTIC EQUATIONS

Ibrahim Aganović, Josip Tambača and Zvonimir Tutek

Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
e-mail: aga@math.hr
e-mail: tambaca@math.hr
e-mail: tutek@math.hr

Abstract.   In this paper we consider the linear elliptic equation of the second order in domains in Rn thin in n - k directions, 0 < k < n. We apply the Ansatz of the formal expansion method (with respect to the small parameter (thickness)) which implies the scaling of the loads in the equation that allows the reduction of the problem from dimension n to dimension k. Appropriate convergence result together with correctors is derived.

2000 Mathematics Subject Classification.   34E05, 35J25.

Key words and phrases.   Reduction dimension, elliptic equation, formal expansion method, Ansatz

Full text (PDF) (free access)

DOI: 10.3336/gm.41.1.08

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