On Homogenization of Nonlinear Robin Type Boundary Conditions for the n-Laplacian in n-Dimensional Perforated Domains

D. Gómez (), E. Pérez (), A. V. Podol’skii () and T. A. Shaposhnikova ()
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D. Gómez: Universidad de Cantabria
E. Pérez: Universidad de Cantabria
A. V. Podol’skii: Moscow State University
T. A. Shaposhnikova: Moscow State University

Chapter Chapter 11 in Integral Methods in Science and Engineering, Volume 1, 2017, pp 119-138 from Springer

Abstract: Abstract We address the homogenization of a boundary value problem posed in perforated media for the p-Laplacian. We consider p = n, that is the n-Laplace operator in a perforated domain of ℝ n $$\mathbb{R}^{n}$$ , n ≥ 3, while the flux (associated with the n-Laplacian) on the boundary of the perforations is given by a negative, nonlinear monotonic function of the solution which is multiplied by a parameter which can be very large compared with the periodicity of the structure O(ɛ). A certain non-periodical distribution of the perforations is allowed, while the assumption that their size is much smaller than the periodicity scale ɛ is performed. We consider different relations between the parameters of the problem and, as ɛ → 0, we obtain all the possible homogenized problems. For certain of these relations, in the average constants of the problem, the perimeter of the perforations appears for any shape.

Date: 2017
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DOI: 10.1007/978-3-319-59384-5_11

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