On boundary value problem with singular inhomogeneity concentrated on the boundary |
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| Authors: | GA Chechkin D Cioranescu A Damlamian AL Piatnitski |
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| Institution: | 1. Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119991, Russia;2. Narvik University College, Postboks 385, 8505 Narvik, Norway;3. Laboratoire Jacques-Louis Lions, Boite courier 187, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France;4. Université Paris-Est, CNRS UMR 8050, Laboratoire d?Analyse et de Mathématiques Appliquées, CMC, 94010 Créteil Cedex, France;5. P.N. Lebedev Physical Institute of RAS, Leninski pr., 53, Moscow 117924, Russia |
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| Abstract: | We study the asymptotic behavior of solutions to a boundary value problem for the Poisson equation with a singular right-hand side, singular potential and with alternating type of the boundary condition. Assuming that the boundary microstructure is periodic, we construct the limit problem and prove the homogenization theorem by means of the unfolding method. The proof requires that the dimension be larger than two. |
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