Cavity type problems ruled by infinity Laplacian operator
  We study a singularly perturbed problem related to infinity Laplacian operator with prescribed boundary values in a region. We prove that solutions are locally (uniformly) Lipschitz continuous, they grow as a linear function, are strongly non-degenerate and have porous level surfaces. Moreover, for some restricted cases we show the finiteness of the (n-1)-dimensional Hausdorff measure of level sets. The analysis of the asymptotic limits is carried out as well. 
Gleydson Chaves Ricarte, Jo\~ao V\'itor da Silva, Rafayel Teymurazyan
math.AP