Differential and Integral Equations

Asymptotic analysis of singular problems in perforated cylinders

Daniela Giachetti, Bogdan Vernescu, and Maria Agostina Vivaldi

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In this paper, we deal with elliptic problems having terms singular in the variable $u$ which represents the solution. The problems are posed in cylinders $\Omega_n^\varepsilon$ of height $2n$ and perforated according to a parameter $\varepsilon$. We study existence, uniqueness and asymptotic behavior of the solutions $u_n^\varepsilon$ as the cylinders become infinite ($n\rightarrow +\infty$) and the size of the holes decreases while the number of the holes increases ($\varepsilon\rightarrow 0$).

Article information

Differential Integral Equations, Volume 29, Number 5/6 (2016), 531-562.

First available in Project Euclid: 9 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J75: Singular elliptic equations 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 80M35: Asymptotic analysis


Giachetti, Daniela; Vernescu, Bogdan; Vivaldi, Maria Agostina. Asymptotic analysis of singular problems in perforated cylinders. Differential Integral Equations 29 (2016), no. 5/6, 531--562. https://projecteuclid.org/euclid.die/1457536890

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