Regularity of solutions for some variational problems subject to a convexity constraint
Regularity of solutions for some variational problems subject to a convexity constraint
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一些受凸性约束的变分问题解的正则性
DOI：
10.1002/cpa.3
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发表时间：
2001
影响因子：
3
通讯作者：
T. Lachand
中科院分区：
文献类型：
--
作者：
G. Carlier;T. Lachand;T. Lachand
本文首先研究了凸函数类中一类椭圆泛函在非齐次Dirichlet边界条件下的极小解。在容许函数的上包络为C1的假设下，证明了极小解的C1正则性。这个条件至少在泛函只依赖于梯度时是最优的[3]。
We first study the minimizers, in the class of convex functions, of an elliptic functional with nonhomogeneous Dirichlet boundary conditions. We prove C1 regularity of the minimizers under the assumption that the upper envelope of admissible functions is C1. This condition is optimal at least when the functional depends only on the gradient [3].