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\(\Gamma\)-convergence of the energy functionals for the variable exponent \(p(\cdot)\)-Laplacian and stability of the minimizers with respect to integrability. (English) Zbl 1409.35026

The authors study the \(\Gamma\)-convergence of the energy functional associated to a Laplace-like equation involving the variable exponent \(p(\cdot)\)-Laplacian. Their main result concerns the stability of the minimizers with respect to“integrability” (i.e. as \(p(\cdot)\) goes to some \(q(\cdot)\)).

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
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