Cavity type problems ruled by infinity Laplacian operator

详细信息    查看全文

• 作者：G.C. Ricarte^a ; ^{ricarte@mat.ufc.br} ; J.V. Silva^b ; ^{jdasilva@dm.uba.ar} ; R. Teymurazyan^c ; ^{rafayel@utexas.edu}
• 关键词：35J60 ; 35J75 ; 35B65 ; 35R35
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：2135-2157
• 全文大小：366 K
• 卷排序：262

文摘

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)(n−1)-dimensional Hausdorff measure of level sets. The analysis of the asymptotic limits is carried out as well.