Non existence of critical scales in the homogenization of the problem with p-Laplace diffusion and nonlinear reaction in the boundary of periodically distributed particles in n-dimensional domains when \(p > n\)
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In previous works, the homogenization of the problem with p-Laplace diffusion and nonlinear reaction in the boundary of periodically distributed particles in n-dimensional domains has been studied in the cases where \(p \le n\). The main trait of the cases \(p \le n\) is the existence of a critical size of the particles, for which the nonlinearity arising of the limit problem does not coincide with the non linear term of the microscopic reaction. The main result of this paper proves that in the case \(p > n\) there exists no critical size.
KeywordsHomogenization p-Laplace diffusion Non-linear boundary reaction Non-critical sizes
Mathematics Subject Classification35B27 35J66 35J60 35J92 35J62
The research of the first two authors was partially supported by the project ref. MTM2014-57113-P of the DGISPI (Spain) and as members of the Research Group MOMAT (Ref. 910480) of the UCM . The research of D. Gómez-Castro was supported by a FPU Grant from the Ministerio de Educación, Cultura y Deporte (Spain).
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