Singular behavior for a multi-parameter periodic Dirichlet problem
نویسندگان
چکیده
We consider a Dirichlet problem for the Poisson equation in periodically perforated domain. The geometry of domain is controlled by two parameters: real number ϵ > 0, proportional to radius holes, and map ϕ, which models shape holes. So, if g denotes boundary datum f datum, we have solution each quadruple ( , ϕ ). Our aim study how depends on ), especially when very small holes narrow points. In contrast with previous works, do not introduce assumption that has zero integral fundamental periodicity cell. This brings certain singular behavior close 0. show that, dimension n ambient space greater than or equal 3, suitable restriction can be represented an analytic ) multiplied factor 1 / − 2 . case = 2, add log times π.
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ژورنال
عنوان ژورنال: Asymptotic Analysis
سال: 2023
ISSN: ['0921-7134', '1875-8576']
DOI: https://doi.org/10.3233/asy-231831