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Asymptotic behaviour of a sequence of Neumann problems. (English) Zbl 0895.35011
The author studies the limit behaviour of Neumann problems on fractured and perforated domains (the excepted closed subsets of the domain “accumulate” on a surface). The main result states that the limit of solutions minimizes a functional whose Euler equation is the same Neumann problem but involving transmission conditions on the “accumulation” surface. The proof is based on \(\Gamma\)-convergence arguments and integral representation theorems.
Reviewer: C.Popa (Iaşi)

MSC:
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35J25 Boundary value problems for second-order elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
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