English

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.

Keywords

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

R2 v1 2026-06-22T16:34:30.424Z