The behavior of solutions to an elliptic equation involving a p-Laplacian and a q-Laplacian for large p
In this paper we study the behavior as p→∞ of solutions up,q to −Δpu−Δqu=0 in a bounded smooth domain Ω with a Lipschitz Dirichlet boundary datum u=g on ∂Ω. We find that there is a uniform limit of a subsequence of solutions, that is, there is pj→∞ such that upj,q→u∞ uniformly in Ω¯ and we prove tha...
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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0362546X_v150_n_p104_Bonheure |
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| Sumario: | In this paper we study the behavior as p→∞ of solutions up,q to −Δpu−Δqu=0 in a bounded smooth domain Ω with a Lipschitz Dirichlet boundary datum u=g on ∂Ω. We find that there is a uniform limit of a subsequence of solutions, that is, there is pj→∞ such that upj,q→u∞ uniformly in Ω¯ and we prove that this limit u∞ is a solution to a variational problem, that, when the Lipschitz constant of the boundary datum is less than or equal to one, is given by the minimization of the Lq-norm of the gradient with a pointwise constraint on the gradient. In addition we show that the limit is a viscosity solution to a limit PDE problem that involves the q-Laplacian and the ∞-Laplacian. © 2016 Elsevier Ltd |
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