Optimization problems for weighted Sobolev constants
Optimization problems for weighted Sobolev constants
复制标题
加权 Sobolev 常数的优化问题
DOI：
10.1007/s00526-006-0075-4
复制
发表时间：
2007
影响因子：
2.1
通讯作者：
A. Wagner
中科院分区：
文献类型：
--
作者：
C. Bandle;A. Wagner
本文研究了一个质量约束下的变分问题。使用惩罚方法，我们证明了最佳形状的存在性。我们将证明极小元是Hölder连续的，并且对于一个大类，它们甚至是Lipschitz连续的。导出了最优区域内部变分不等式形式的必要条件和自由边界条件。
In this paper, we study a variational problem under a constraint on the mass. Using a penalty method we prove the existence of an optimal shape. It will be shown that the minimizers are Hölder continuous and that for a large class they are even Lipschitz continuous. Necessary conditions in form of a variational inequality in the interior of the optimal domain and a condition on the free boundary are derived.