engleski

A note on reduction of dimension for linear elliptic equations

In this paper we consider the linear elliptic equation of the second order in domains in R^n 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.

Reduction dimension; elliptic equation; formal expansion method; Ansatz

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