Special cases of the planar least gradient problem

详细信息    查看全文

• 作者：Wojciech Gó ; rny^a ; Piotr Rybka^a ; ^b ; ^{rybka@mimuw.edu.pl} ; Ahmad Sabra^a
• 关键词：primary ; 49J10 ; secondary ; 49Q10 ; 49J20 ; 35A15
• 刊名：Nonlinear Analysis: Theory, Methods & Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：151
• 期：Complete
• 页码：66-95
• 全文大小：1084 K
• 卷排序：151

文摘

We study two special cases of the planar least gradient problem. In the first one, the boundary conditions are imposed on a part of a strictly convex domain. In the second case, we impose the Dirichlet data on the boundary of a rectangle, an example of convex but not strictly convex domain. We show the existence of solutions and study their properties for particular cases of boundary data.