Cavity type problems ruled by infinity Laplacian operator
Analysis of PDEs
2016-10-28 v1
Abstract
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.
Cite
@article{arxiv.1610.08949,
title = {Cavity type problems ruled by infinity Laplacian operator},
author = {Gleydson Chaves Ricarte and João Vítor da Silva and Rafayel Teymurazyan},
journal= {arXiv preprint arXiv:1610.08949},
year = {2016}
}
Comments
22 pages