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arXiv · 1811.03863

Limit of p-Laplacian Obstacle problems

Raffaela Capitanelli·Maria Agostina Vivaldi
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Abstract

In this paper we study asymptotic behavior of solutions of obstacle problems for $p-$Laplacians as $p\to \infty.$ For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of whole family of the solutions of obstacle problems either for data $f$ that change sign in $Ω$ or for data $f$ (that do not change sign in $Ω$) possibly vanishing in a set of positive measure.

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Raffaela Capitanelli, Maria Agostina Vivaldi. 2020-05-24. Limit of p-Laplacian Obstacle problems. https://doi.org/10.1515/acv-2019-0058

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