论文标题
一个抽象的INF-SUP问题，灵感受到完美可塑性和相关应用中极限分析的启发
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications
论文作者
论文摘要
这项工作涉及双线拉格朗日和凸限制产生的抽象INF-SUP问题。我们研究了保证INF-SUP和相关SUP-INF问题之间没有差距的条件。本文中引入的关键假设概括了众所周知的Babuska-Brezzi条件。它基于功能空间中凸锥定义的INF-SUP条件。我们还采用了一种正则化方法来解决INF-SUP问题并得出临界值（INF-SUP）值的可计算大专长，该值可用于数值结果的后验错误分析。抽象问题获得的结果应用于连续力学。特别是，引入了经典可塑性，梯度可塑性和分层引起的极限载荷问题的示例。
This work is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuska-Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular, examples of limit load problems and similar ones arising in classical plasticity, gradient plasticity and delamination are introduced.
