Scholarlink

<p>Lower semicontinuity is a key continuity concept in set-valued analysis, but it is also known to be somehow difficult to establish when one wants to tackle specific set-valued maps like constraint maps of quasi-variational inequalities or generalized Nash equilibrium problems or quasi-optimization problems. A classical sufficient condition to obtain the lower semicontinuity is the openness of the graph of the map or of its fibers. Our aim in this work is to propose a weaker concept, called <i>densely locally constant</i>, ensuring the lower semicontinuity and, at the same time, with powerful properties like local intersection property or stability over convexification. Moreover, this new concept allows us to prove alternative selection results, fixed-point theorems and the maximum principle.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Toward Tractable Conditions for Lower Semicontinuity of Set-Valued Maps: Concepts and Applications

  • 期刊论文

  • 发表日期：

    2026年3月14日

查看全文
  • Didier Aussel,
  • Orestes Bueno,
  • Carlos Calderón,
  • John Cotrina

摘要

Lower semicontinuity is a key continuity concept in set-valued analysis, but it is also known to be somehow difficult to establish when one wants to tackle specific set-valued maps like constraint maps of quasi-variational inequalities or generalized Nash equilibrium problems or quasi-optimization problems. A classical sufficient condition to obtain the lower semicontinuity is the openness of the graph of the map or of its fibers. Our aim in this work is to propose a weaker concept, called densely locally constant, ensuring the lower semicontinuity and, at the same time, with powerful properties like local intersection property or stability over convexification. Moreover, this new concept allows us to prove alternative selection results, fixed-point theorems and the maximum principle.