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- W2559053720 abstract "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." @default.
- W2559053720 created "2016-12-08" @default.
- W2559053720 creator A5033040146 @default.
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- W2559053720 date "2017-02-01" @default.
- W2559053720 modified "2023-10-17" @default.
- W2559053720 title "The behavior of solutions to an elliptic equation involving a <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mi>p</mml:mi></mml:math>-Laplacian and a <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si2.gif display=inline overflow=scroll><mml:mi>q</mml:mi></mml:math>-Laplacian for large <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mi>p</mml…" @default.
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- W2559053720 doi "https://doi.org/10.1016/j.na.2016.11.001" @default.
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