Article
Asymptotic behavior of nonlinear elliptic systems on varying domains
Author/s | Casado Díaz, Juan
Garroni, Adriana |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2000 |
Deposit Date | 2016-09-30 |
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Abstract | We consider a monotone operator of the form Au = −div(a(x, Du)), with Ω ⊆ Rn and a : Ω×MM×N → MM×N , acting on W1,p 0 (Ω, RM). For every sequence (Ωh) of open subsets of Ω and for every f ∈ W−1,p0 (Ω, RM), 1/p+ 1/p0 = 1, ... We consider a monotone operator of the form Au = −div(a(x, Du)), with Ω ⊆ Rn and a : Ω×MM×N → MM×N , acting on W1,p 0 (Ω, RM). For every sequence (Ωh) of open subsets of Ω and for every f ∈ W−1,p0 (Ω, RM), 1/p+ 1/p0 = 1, we study the asymptotic behavior, as h → +∞, of the solutions uh ∈ W1 0 (Ωh, RM) of the systems Auh = f in W−1,p0 (Ωh, RM), and we determine the general form of the limit problem. |
Citation | Casado Díaz, J. y Garroni, A. (2000). Asymptotic behavior of nonlinear elliptic systems on varying domains. SIAM Journal on Mathematical Analysis, 31 (3), 581-624. |
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