Homogenization of quasi-linear equations with natural growth terms |
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Authors: | Valeria Chiadò Piat Anneliese Defranceschi |
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Affiliation: | (1) SISSA, Strada Costiera 11, 34014 Trieste, (Italy) |
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Abstract: | In this paper we deal with the limit behaviour of the bounded solutions uε of quasi-linear equations of the form of Ω with Dirichlet boundary conditions on σΩ. The map a=a(x,ϕ) is periodic in x, monotone in ϕ, and satisfies suitable coerciveness and growth conditions. The function H=H(x,s,ϕ) is assumed to be periodic in x, continuous in [s,ϕ] and to grow at most like |ξ|p. Under these assumptions on a and H we prove that there exists a function H0=H0(s,ϕ) with the same behaviour of H, such that, up to a subsequence, (uε) converges to a solution u of the homogenized problem -div(b(Du)) + γ|u|p-2u = H0(u,Du) + h(x) on Ω, where b depends only on a and has analogous qualitative properties. |
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