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We study a singularly perturbed problem related to infinity Laplacianoperator with prescribed boundary values in a region. We prove that solutionsare locally (uniformly) Lipschitz continuous, they grow as a linear function,are strongly non-degenerate and have porous level surfaces. Moreover, for somerestricted cases we show the finiteness of the (n-1)-dimensional Hausdorffmeasure of level sets. The analysis of the asymptotic limits is carried out aswell.

Cavity type problems ruled by infinity Laplacian operator